ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 24 Feb 2020 18:43:05 GMT2020-02-24T18:43:05Z50381- Increasing thermoelectric efficiency: Dynamical models unveil microscopic mechanismshttps://scholarbank.nus.edu.sg/handle/10635/117049Title: Increasing thermoelectric efficiency: Dynamical models unveil microscopic mechanisms
Authors: Benenti, G.; Casati, G.
Abstract: Dynamical nonlinear systems provide a new approach to the old problem of increasing the efficiency of thermoelectric machines. In this review, we discuss stylized models of classical dynamics, including non-interacting complex molecules in an ergodic billiard, A disordered hard-point gas and an abstract thermoelectric machine. The main focus will be on the physical mechanisms, unveiled by these dynamical models, which lead to high thermoelectric efficiency approaching the Carnot limit. This journal is © 2011 The Royal Society.
Fri, 28 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1170492011-01-28T00:00:00Z
- Quantum dephasing and decay of classical correlation functions in chaotic systemshttps://scholarbank.nus.edu.sg/handle/10635/97671Title: Quantum dephasing and decay of classical correlation functions in chaotic systems
Authors: Sokolov, V.V.; Benenti, G.; Casati, G.
Abstract: We discuss the dephasing induced by internal classical chaotic motion in the absence of any external environment. To this end an extension of fidelity for mixed states is introduced, which we name allegiance. Such a quantity directly accounts for quantum interference and is measurable in a Ramsey interferometry experiment. We show that in the semiclassical limit the decay of the allegiance is exactly expressed, due to the dephasing, in terms of an appropriate classical correlation function. Our results are derived analytically for the case of a nonlinear driven oscillator and then numerically confirmed for the kicked rotor model. © 2007 The American Physical Society.
Fri, 23 Feb 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/976712007-02-23T00:00:00Z
- Stability of quantum motion in regular systems: A uniform semiclassical approachhttps://scholarbank.nus.edu.sg/handle/10635/98012Title: Stability of quantum motion in regular systems: A uniform semiclassical approach
Authors: Wang, W.-G.; Casati, G.; Li, B.
Abstract: We study the stability of quantum motion of classically regular systems in the presence of small perturbations. On the basis of a uniform semiclassical theory we derive the fidelity decay which displays a quite complex behavior, from Gaussian to power law decay t-α, with 1≤α≤2. Semiclassical estimates are given for the time scales separating the different decaying regions, and numerical results are presented which confirm our theoretical predictions. © 2007 The American Physical Society.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/980122007-01-01T00:00:00Z
- Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensateshttps://scholarbank.nus.edu.sg/handle/10635/97704Title: Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensates
Authors: Casati, G.; Poletti, D.
Abstract: We study cold atoms and Bose-Einstein condensates exposed to time-dependent standing waves of light. We first discuss a quantum chaotic dissipative ratchet using the method of quantum trajectories. This system is characterized by directed transport emerging from a quantum strange attractor. We then present a very simple model of directed transport with cold atoms in a pair of periodically flashed optical lattices. Finally we study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We show that the many-body atom-atom interactions, treated within the mean-field approximation, can generate directed transport. © 2007 IOP Publishing Ltd.
Tue, 01 May 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/977042007-05-01T00:00:00Z
- Thermal diode: Rectification of heat fluxhttps://scholarbank.nus.edu.sg/handle/10635/115996Title: Thermal diode: Rectification of heat flux
Authors: Li, B.; Wang, L.; Casati, G.
Abstract: A thermal diode model that works in a wide range of system parameters was demonstrated by coupling two nonlinear one dimensional lattices. A numerical and anlytical evidence for the mechanism which allows heat flux in one direction while the system acts like an insulator when the temperature gradient was reversed was also provided. The study of possible experimental realization in nanoscale systems was briefly discussed. It was shown that in the high temperature limit the on-site potential can be neglected and the system was close to 2 coupled harmonic chains.
Fri, 29 Oct 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159962004-10-29T00:00:00Z
- Fourier law in the alternate-mass hard-core potential chainhttps://scholarbank.nus.edu.sg/handle/10635/111404Title: Fourier law in the alternate-mass hard-core potential chain
Authors: Li, B.; Casati, G.; Wang, J.; Prosen, T.
Abstract: The energy transport in a one-dimensional model of elastically colliding particles with alternate mass and the validity of Fourier Law were studied. A marginally stable interacting many particle system was considered for studying the diffusive energy transport. It was stated that the exponential dynamical instability was not necessary for the establishment of Fourier Law. It was found that the validity of Fourier Law was influenced by the breaking of total momentum conservation.
Fri, 25 Jun 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1114042004-06-25T00:00:00Z
- Universal decay of the classical Loschmidt echo of neutrally stable mixing dynamicshttps://scholarbank.nus.edu.sg/handle/10635/98524Title: Universal decay of the classical Loschmidt echo of neutrally stable mixing dynamics
Authors: Casati, G.; Prosen, T.; Lan, J.; Li, B.
Abstract: We provide analytical and numerical evidence that the classical mixing systems, which lack exponential sensitivity on initial conditions, exhibit universal decay of the Loschmidt echo which turns out to be a function of a single scaled time variable δ2/5t, where δ is the strength of perturbation. The role of dynamical instability and entropy production is discussed. © 2005 The American Physical Society.
Fri, 25 Mar 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/985242005-03-25T00:00:00Z
- Entanglement-induced decoherence and energy eigenstateshttps://scholarbank.nus.edu.sg/handle/10635/96497Title: Entanglement-induced decoherence and energy eigenstates
Authors: Wang, W.-G.; Gong, J.; Casati, G.; Li, B.
Abstract: Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help with understanding the dynamics of quantum entanglement generation in chaotic quantum systems. © 2008 The American Physical Society.
Tue, 22 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/964972008-01-22T00:00:00Z
- One-dimensional hard-point gas as a thermoelectric enginehttps://scholarbank.nus.edu.sg/handle/10635/111457Title: One-dimensional hard-point gas as a thermoelectric engine
Authors: Wang, J.; Casati, G.; Prosen, T.; Lai, C.-H.
Abstract: We demonstrate the possibility to build a thermoelectric engine using a one-dimensional gas of molecules with unequal masses and hard-point interaction. Most importantly, we show that the efficiency of this engine is determined by a parameter YT which is different from the well known figure of merit ZT. Even though the efficiency of this particular model is low, our results shed light on the problem and open the possibility to build efficient thermoelectric engines. © 2009 The American Physical Society.
Thu, 24 Sep 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1114572009-09-24T00:00:00Z
- Thermalization and ergodicity in one-dimensional many-body open quantum systemshttps://scholarbank.nus.edu.sg/handle/10635/112533Title: Thermalization and ergodicity in one-dimensional many-body open quantum systems
Authors: Žnidarič, M.; Prosen, T.; Benenti, G.; Casati, G.; Rossini, D.
Abstract: Using an approach based on the time-dependent density-matrix renormalization-group method, we study the thermalization in spin chains locally coupled to an external bath. Our results provide evidence that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well approximated by the grand canonical state. Moreover, the resulting ergodic state in the bulk does not depend on the details of the baths. On the other hand, for integrable systems we found that the invariant state in general depends on the bath and is different from the grand canonical state. © 2010 The American Physical Society.
Thu, 27 May 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125332010-05-27T00:00:00Z
- A microscopic mechanism for increasing thermoelectric efficiencyhttps://scholarbank.nus.edu.sg/handle/10635/115560Title: A microscopic mechanism for increasing thermoelectric efficiency
Authors: Saito, K.; Benenti, G.; Casati, G.
Abstract: We study the coupled particle and energy transport in a prototype model of interacting one-dimensional system: the disordered hard-point gas, for which numerical data suggest that the thermoelectric figure of merit ZT diverges with the system size. This result is explained in terms of a microscopic mechanism, namely the local equilibrium is characterized by the emergence of a broad stationary "modified Maxwell-Boltzmann velocity distribution", of width much larger than the mean velocity of the particle flow. © 2010 Elsevier B.V. All rights reserved.
Tue, 05 Oct 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1155602010-10-05T00:00:00Z
- Thermopower with broken time-reversal symmetryhttps://scholarbank.nus.edu.sg/handle/10635/112534Title: Thermopower with broken time-reversal symmetry
Authors: Saito, K.; Benenti, G.; Casati, G.; Prosen, T.
Abstract: We show that when inelastic scattering effects are taken into account, the thermopower is, in general, asymmetric under magnetic field reversal, even for noninteracting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux. © 2011 American Physical Society.
Mon, 14 Nov 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125342011-11-14T00:00:00Z
- Ratchet effect and the transporting Islands in the chaotic seahttps://scholarbank.nus.edu.sg/handle/10635/97757Title: Ratchet effect and the transporting Islands in the chaotic sea
Authors: Wang, L.; Benenti, G.; Casati, G.; Li, B.
Abstract: We study directed transport in a classical deterministic dissipative system. We consider the generic case of mixed phase space and show that large ratchet currents can be generated thanks to the presence, in the Hamiltonian limit, of transporting stability islands embedded in the chaotic sea. Because of the simultaneous presence of chaos and dissipation the stationary value of the current is independent of initial conditions, except for initial states with very small measure. © 2007 The American Physical Society.
Fri, 14 Dec 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/977572007-12-14T00:00:00Z
- Complexity of quantum states and reversibility of quantum motionhttps://scholarbank.nus.edu.sg/handle/10635/96044Title: Complexity of quantum states and reversibility of quantum motion
Authors: Sokolov, V.V.; Zhirov, O.V.; Benenti, G.; Casati, G.
Abstract: We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number M (t) of harmonics of the [initially isotropic, i.e., M (0) =0] Wigner function, which are generated during quantum evolution for the time t. We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment T immediately after applying at this moment an instant perturbation governed by a strength parameter ξ. It follows that there exists a critical perturbation strength ξc ≈ 2/M (T) below which the initial state is well recovered, whereas reversibility disappears when ξ ξc (T). In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model. © 2008 The American Physical Society.
Tue, 21 Oct 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960442008-10-21T00:00:00Z
- Interaction-induced quantum ratchet in a Bose-Einstein condensatehttps://scholarbank.nus.edu.sg/handle/10635/96952Title: Interaction-induced quantum ratchet in a Bose-Einstein condensate
Authors: Poletti, D.; Benenti, G.; Casati, G.; Li, B.
Abstract: We study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We first prove that in the noninteracting case this system can present a quantum symmetry which forbids the ratchet effect classically expected. We then show how many-body atom-atom interactions, treated within the mean-field approximation, can break this quantum symmetry, thus generating directed transport. © 2007 The American Physical Society.
Fri, 24 Aug 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/969522007-08-24T00:00:00Z
- Comment on "coherent ratchets in driven Bose-Einstein condensates"https://scholarbank.nus.edu.sg/handle/10635/115526Title: Comment on "coherent ratchets in driven Bose-Einstein condensates"
Authors: Benenti, G.; Casati, G.; Denisov, S.; Flach, S.; Hänggi, P.; Li, B.; Poletti, D.
Thu, 03 Jun 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1155262010-06-03T00:00:00Z
- Negative differential conductivity in far-from-equilibrium quantum spin chainshttps://scholarbank.nus.edu.sg/handle/10635/112469Title: Negative differential conductivity in far-from-equilibrium quantum spin chains
Authors: Benenti, G.; Casati, G.; Prosen, T.; Rossini, D.
Abstract: We show that, when a finite anisotropic Heisenberg spin-1/2 chain in the gapped regime is driven far from equilibrium, oppositely polarized ferromagnetic domains build up at the edges of the chain, thus suppressing quantum spin transport. As a consequence, a negative differential conductivity regime arises, where increasing the driving decreases the current. The above results are explained in terms of magnon localization and are shown to be structurally stable against breaking of integrability. Copyright © 2009 EPLA.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124692009-01-01T00:00:00Z
- Magnetically induced thermal rectificationhttps://scholarbank.nus.edu.sg/handle/10635/97129Title: Magnetically induced thermal rectification
Authors: Casati, G.; Mejía-Monasterio, C.; Prosen, T.
Abstract: We consider far from equilibrium heat transport in chaotic billiard chains with noninteracting charged particles in the presence of nonuniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths. © 2007 The American Physical Society.
Thu, 08 Mar 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/971292007-03-08T00:00:00Z
- Quantum chaos and the double-slit experimenthttps://scholarbank.nus.edu.sg/handle/10635/97665Title: Quantum chaos and the double-slit experiment
Authors: Casati, G.; Prosen, T.
Abstract: We report on the numerical simulation of the double-slit experiment, where the initial wave packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior. © 2005 The American Physical Society.
Thu, 01 Sep 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/976652005-09-01T00:00:00Z
- Negative differential thermal resistance and thermal transistorhttps://scholarbank.nus.edu.sg/handle/10635/97305Title: Negative differential thermal resistance and thermal transistor
Authors: Li, B.; Wang, L.; Casati, G.
Abstract: We report on the first model of a thermal transistor to control heat flow. Like its electronic counterpart, our thermal transistor is a three-terminal device with the important feature that the current through the two terminals can be controlled by small changes in the temperature or in the current through the third terminal. This control feature allows us to switch the device between "off" (insulating) and "on" (conducting) states or to amplify a small current. The thermal transistor model is possible because of the negative differential thermal resistance. © 2006 American Institute of Physics.
Mon, 03 Apr 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973052006-04-03T00:00:00Z
- Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equationshttps://scholarbank.nus.edu.sg/handle/10635/97330Title: Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equations
Authors: Yan, Y.; Wu, C.-Q.; Casati, G.; Prosen, T.; Li, B.
Abstract: We numerically investigate the heat conduction in a random-exchange Ising spin chain by using the quantum master equation. The chain is subject to a uniform transverse field h, while the exchange couplings { Qn } between the nearest neighbor spins are random; the largest size we simulate is up to 10. This model is integrable; i.e., the nearest neighbor level spacing distribution is Poissonian. However, we find clear evidence of nonballistic transport. In the small coupling regime (Qn h), an energy and/or temperature gradient in the bulk of the system is observed and the energy current appears to be proportional to the inverse of the system size. Moreover, we find that in the low and high temperature regimes, the thermal conductivity κ and the specific heat Cv have the same dependence on temperature. The large coupling case (Qn ∼h) is also discussed. © 2008 The American Physical Society.
Fri, 23 May 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973302008-05-23T00:00:00Z
- Conservative chaotic map as a model of quantum many-body environmenthttps://scholarbank.nus.edu.sg/handle/10635/96069Title: Conservative chaotic map as a model of quantum many-body environment
Authors: Rossini, D.; Benenti, G.; Casati, G.
Abstract: We study the dynamics of the entanglement between two qubits coupled to a common chaotic environment, described by the quantum kicked rotator model. We show that the kicked rotator, which is a single-particle deterministic dynamical system, can reproduce the effects of a pure dephasing many-body bath. Indeed, in the semiclassical limit the interaction with the kicked rotator can be described as a random phase kick, so that decoherence is induced in the two-qubit system. We also show that our model can efficiently simulate non-Markovian environments. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960692006-01-01T00:00:00Z
- Uniform semiclassical approach to fidelity decay in the deep Lyapunov regimehttps://scholarbank.nus.edu.sg/handle/10635/98520Title: Uniform semiclassical approach to fidelity decay in the deep Lyapunov regime
Authors: Wang, W.-G.; Casati, G.; Li, B.; Prosen, T.
Abstract: We use the uniform semiclassical approximation in order to derive the fidelity decay in the regime of large perturbations. Numerical computations are presented which agree with our theoretical predictions. Moreover, our theory allows us to explain previous findings, such as the deviation from the Lyapunov decay rate in cases where the classical finite-time instability is nonuniform in phase space. ©2005 The American Physical Society.
Tue, 01 Mar 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/985202005-03-01T00:00:00Z
- Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibriumhttps://scholarbank.nus.edu.sg/handle/10635/112393Title: Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
Authors: Benenti, G.; Casati, G.; Prosen, T.; Rossini, D.; Žnidarič, M.
Abstract: We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the t-V spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism. © 2009 The American Physical Society.
Thu, 06 Aug 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1123932009-08-06T00:00:00Z
- Asymmetric wave propagation in nonlinear systemshttps://scholarbank.nus.edu.sg/handle/10635/112383Title: Asymmetric wave propagation in nonlinear systems
Authors: Lepri, S.; Casati, G.
Abstract: A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schrödinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect. © 2011 American Physical Society.
Mon, 18 Apr 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1123832011-04-18T00:00:00Z
- Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical latticeshttps://scholarbank.nus.edu.sg/handle/10635/95949Title: Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical lattices
Authors: Carlo, G.G.; Benenti, G.; Casati, G.; Wimberger, S.; Morsch, O.; Mannella, R.; Arimondo, E.
Abstract: We present a very simple model for realizing directed transport with cold atoms in a pair of periodically flashed optical lattices. The origin of this ratchet effect is explained and its robustness demonstrated under imperfections typical of cold atom experiments. We conclude that our model offers a clear-cut way to implement directed transport in an atom optical experiment. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/959492006-01-01T00:00:00Z
- Nonequilibrium properties of the one-dimensional hard-point gas systemhttps://scholarbank.nus.edu.sg/handle/10635/97338Title: Nonequilibrium properties of the one-dimensional hard-point gas system
Authors: Casati, G.; Prosen, T.; Wang, L.; Li, B.
Abstract: We discuss the stability properties of a one-dimensional hard-point gas. We study the decay of the Loschmidt echo which describes the stability of the motion under system perturbations. We show a universal behavior in the echo decay which is intimately connected to the linear dynamical instability of the motion. In particular, in spite of such a weak instability, the asymptotic decay follows a simple exponential law. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973382006-01-01T00:00:00Z
- Linear instability and statistical laws of physicshttps://scholarbank.nus.edu.sg/handle/10635/97068Title: Linear instability and statistical laws of physics
Authors: Casati, G.; Tsallis, C.; Baldovin, F.
Abstract: We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, i) the sensitivity to initial conditions is given by ξ = [1 + (1 - q)λqt]1/(1-q) with q = 0; ii) the statistical entropy Sq = (1 - ∑ipi q)/(q-1) (S1 = - ∑ipilnpi) in the infinitely fine graining limit (i.e., W ≡ number of cells into which the phase space has been partitioned → ∞), increases linearly with time only for q = 0; iii) a nontrivial, q-generalized, Pesin-like identity is satisfied, namely the limt→∞ limW→∞ S0(t)/t = max{λ0}. These facts (which are in analogy to the usual behaviour of strongly chaotic systems with q = 1), seem to open the door for a statistical description of conservative many-body nonlinear systems whose Lyapunov spectrum vanishes. © EDP Sciences.
Tue, 01 Nov 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/970682005-11-01T00:00:00Z
- Fourier's law in a quantum spin chain and the onset of quantum chaoshttps://scholarbank.nus.edu.sg/handle/10635/96672Title: Fourier's law in a quantum spin chain and the onset of quantum chaos
Authors: Mejía-Monasterio, C.; Prosen, T.; Casati, G.
Abstract: We study heat transport in a nonequilibrium steady state of a quantum interacting spin chain. We provide clear numerical evidence of the validity of Fourier law. The regime of normal conductivity is shown to set in at the transition to quantum chaos. © EDP Sciences.
Tue, 15 Nov 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/966722005-11-15T00:00:00Z
- Detecting entanglement of random states with an entanglement witnesshttps://scholarbank.nus.edu.sg/handle/10635/96182Title: Detecting entanglement of random states with an entanglement witness
Authors: Žnidarič, M.; Prosen, T.; Benenti, G.; Casati, G.
Abstract: The entanglement content of high-dimensional random pure states is almost maximal; nevertheless, we show that, due to the complexity of such states, the detection of their entanglement using witness operators is rather difficult. We discuss the case of unknown random states, and the case of known random states for which we can optimize the entanglement witness. Moreover, we show that coarse graining, modelled by considering mixtures of m random states instead of pure ones, leads to a decay in the entanglement detection probability exponential with m. Our results also allow us to explain the emergence of classicality in coarse grained quantum chaotic dynamics. © 2007 IOP Publishing Ltd.
Fri, 09 Nov 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/961822007-11-09T00:00:00Z
- How complex is quantum motion?https://scholarbank.nus.edu.sg/handle/10635/112450Title: How complex is quantum motion?
Authors: Benenti, G.; Casati, G.
Abstract: In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties. © 2009 The American Physical Society.
Mon, 02 Feb 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124502009-02-02T00:00:00Z
- Stability of quantum motion: Beyond Fermi-golden-rule and Lyapunov decayhttps://scholarbank.nus.edu.sg/handle/10635/98013Title: Stability of quantum motion: Beyond Fermi-golden-rule and Lyapunov decay
Authors: Wang, W.-G.; Casati, G.; Li, B.
Abstract: The stability of quantum motion for a classically chaotic system is discussed. The existence of different regimes of fidelity decay is shown. The deviations from Fermi-golden-rule and Lyapunov regimes are observed when the underlying classical dynamics is weakly chaotic. It is found that fidelity is an important quantity which characterizes the stability of quantum and classical systems.
Sun, 01 Feb 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/980132004-02-01T00:00:00Z
- Device physics: The heat is on - And offhttps://scholarbank.nus.edu.sg/handle/10635/96210Title: Device physics: The heat is on - And off
Authors: Casati, G.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/962102007-01-01T00:00:00Z
- Phase-space characterization of complexity in quantum many-body dynamicshttps://scholarbank.nus.edu.sg/handle/10635/112484Title: Phase-space characterization of complexity in quantum many-body dynamics
Authors: Balachandran, V.; Benenti, G.; Casati, G.; Gong, J.
Abstract: We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well-known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase in entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long-term fluctuations which become smaller when quantum chaos sets in. © 2010 The American Physical Society.
Wed, 20 Oct 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124842010-10-20T00:00:00Z
- Heat conductivity in linear mixing systemshttps://scholarbank.nus.edu.sg/handle/10635/116383Title: Heat conductivity in linear mixing systems
Authors: Li, B.; Casati, G.; Wang, J.
Abstract: A study of heat conductivity in linear mixing system was carried out. A quasi-one-dimensional channel with triangular scatterers with internal angles was also investigated. The numerical value of the thermal conductivity computed via a Green-Kubo approach agrees with that obtained by direct numerical simulations with thermal baths.
Sat, 01 Feb 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1163832003-02-01T00:00:00Z
- Dynamical chaos and decoherencehttps://scholarbank.nus.edu.sg/handle/10635/98674Title: Dynamical chaos and decoherence
Authors: Casati, G.; Rossini, D.
Abstract: Fidelity is a convenient tool to study the sensitivity of quantum motion under Hamiltonian perturbations. In this paper we first show that classical chaos can produce the dephasing necessary to suppress quantum interference, even in the absence of any environment. To this end we consider the fidelity of mixed states, which takes into account interference amplitudes, and directly relate its decay to the decay of an appropriate classical correlation function, which is totally unrelated to quantum phases. We then discuss the dephasing in a two-qubit system, induced by the coupling to a single-particle, deterministic chaotic environment. The latter is shown to behave as a pure dephasing many-body object which induces decoherence in the system; memory effects are also taken into account.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/986742007-01-01T00:00:00Z
- Heat flow in classical and quantum systems and thermal rectificationhttps://scholarbank.nus.edu.sg/handle/10635/98734Title: Heat flow in classical and quantum systems and thermal rectification
Authors: Casati, G.; Mejía-Monasterio, C.
Abstract: The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction may lead to potentially interesting applications based on the possibility to control the heat flow. Indeed, different models of thermal rectifiers has been recently proposed in which heat can flow preferentially in one direction. Although these models are far away from a prototype realization, the underlying mechanisms are of very general nature and, as such, are suitable of improvement and may eventually lead to real applications. We briefly discuss the problem of heat transport in classical and quantum systems and its relation to the chaoticity of the dynamics. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow. © 2007 American Institute of Physics.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/987342007-01-01T00:00:00Z
- Classical and quantum chaos and control of heat flowhttps://scholarbank.nus.edu.sg/handle/10635/95990Title: Classical and quantum chaos and control of heat flow
Authors: Casati, G.; Mejía-Monasterio, C.
Abstract: We discuss the problem of heat conduction in classical and quantum low-dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of the Fourier law of heat conduction in linear mixing systems, i.e., in systems without exponential instability. At the quantum level, where motion is characterized by the lack of exponential dynamical instability, we show that the validity of the Fourier law is in direct relation to the onset of quantum chaos. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow. The control of heat conduction by nonlinearity opens the possibility to propose new devices, such as a thermal rectifier.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/959902007-01-01T00:00:00Z