Nonequilibrium Phenomena in Nonlinear Lattices: From Slow Relaxation to Anomalous Transport

Iubini, Stefano; Lepri, Stefano; Livi, Roberto; Politi, Antonio; Politi, Paolo

doi:10.1007/978-3-030-44992-6_8

Cited by 7 publications

(12 citation statements)

References 83 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamical freezing of relaxation due to breather states in the DNLS equation was studied in detail in [97,189] in a simplified setup. In particular, it was performed a statistical study of the relaxation of a single breather on a background thermalized at positive temperature.…”

Section: B Slow Relaxation To Equilibriummentioning

confidence: 99%

Statistical Mechanics of Systems with Negative Temperature

Baldovin,

Iubini,

Livi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

I. Introduction A. Introductory remarks and plan of the paper B. Entropy and temperature C. Negative absolute temperature II. Examples and phenomenology A. Onsager's vortices B. Magnetic systems C. Laser systems D. Cold atoms in optical lattices E. Discrete Nonlinear Schrödinger Equation III. Alternative interpretations A. Two definitions of entropy (and temperature) B. Main properties of Gibbs' formalism 1. Equipartition theorem 2. Exact validity of the Thermodynamic Relations 3. Adiabatic invariance of the entropy 4. Helmholtz's theorem C. The debate about negative temperature 1. Critics of Boltzmann entropy 2. In defense of Boltzmann's formalism and negative temperature 3. The problem of thermodynamic cycles 4. Critics of negative-temperature equilibrium 5. Remarks IV. Equilibrium at β < 0 A. The problem of measuring temperature B. Zeroth law and thermometry C. Ensemble equivalence (and its violations) 1. Simple models 2. A wider scenario V. Fluctuation-dissipation and response theory A. Langevin equation with β < 0 B. Thermal baths at negative temperature C. Response theory VI. Non-equilibrium and localization in the DNLS chain A. Ensemble inequivalence B. Slow relaxation to equilibrium VII. Fourier transport A. Simple one-dimensional models 1. Spin chain: equilibrium properties 2. Spin chain: heat transport 3. Other examples and remarks B. DNLS equation VIII. Conclusions

show abstract

Section: B Slow Relaxation To Equilibriummentioning

confidence: 99%

Statistical Mechanics of Systems with Negative Temperature

Baldovin,

Iubini,

Livi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The utility of such a representation in the study of periodic solution of the undamped dNLS equation was noted at least as long ago as [13]. Since we are interested in studying the energy of the system, we can look at the energy of each site individually, defined by E j (t) = 1 2 |z j (t)| 2 . The system can be represented using these energies and the complex phase.…”

Section: The "Twist" Of the Breathersmentioning

confidence: 99%

“…Here, A (ω, ) and B (ω, ) are N × N tri-diagonal matrices and D (1) and D (2) are N × N diagonal matrices. More precisely, the matrix A (ω, ) has on the sub-and super-diagonal, while the diagonal elements are ω−a j −(p * j ) 2 −3(q * j ) 3 , j = 1, 2, .…”

Section: Stabilitymentioning

confidence: 99%

“…In this paper we reexamine the existence and properties of metastable states in (finite) lattices of coupled nonlinear oscillators. Systems of this type have often been used to study energy transport in extended systems and in both stochastic and deterministic versions of these systems it has been observed that the solution can be "trapped" for long times in small regions of the phase space, which in turn affects the length of time it takes for the system to exhibit ergodic properties -in some cases making that time scale so long that these properties are effectively unobservable [1] [2] [3], [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Damped and Driven Breathers and Metastability

Caballero¹,

Wayne²

2021

Preprint

View full text Add to dashboard Cite

In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrödinger equations subject to spatially localized driving and damping and we show numerically that they provide a more accurate approximation to metastable states in these systems than previous proposals. We also study the stability properties of these solutions and show that they fit well with a previously proposed mechanism for the emergence and persistence of metastable behavior.

show abstract

“…The ratio of these quantities in absolute value is a function of the local temperature and is called thermal conductivity. A particular subclass of models has attracted attention in the mathematical and theoretical physics literature on thermal transport already at the end of the 1990s, namely one dimensional chains of atoms (see the review articles [8,16,20]). The idea was to consider the simplest possible model to understand the sufficient and/or necessary ingredients for Fourier's law to hold.…”

Section: Introductionmentioning

confidence: 99%

Thermo-mechanical Transport in Rotor Chains

2021

View full text Add to dashboard Cite

We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic dynamics, we perform extensive numerical computations based on a finite difference method for the system of partial differential equations describing the macroscopic steady state. We first present a formal derivation of these stationary equations based on a linear response argument and local equilibrium assumptions. We then study various properties of the solutions of these equations. This allows to characterize the regime of parameters leading to uphill energy diffusion-a situation in which the energy flows in the direction of the gradient of temperature-and to identify regions of parameters corresponding to a negative energy conductivity (i.e. a positive linear response of the energy current to a gradient of temperature). The macroscopic equations we derive are consistent with some previous results obtained by numerical simulation of the microscopic physical system, which confirms their validity. KeywordsThermal transport • Rotor chain • Thermo-mechanical response • Macroscopic diffusion equations • Uphill diffusion B Alessandra Iacobucci

show abstract

Nonequilibrium Phenomena in Nonlinear Lattices: From Slow Relaxation to Anomalous Transport

Cited by 7 publications

References 83 publications

Statistical Mechanics of Systems with Negative Temperature

Statistical Mechanics of Systems with Negative Temperature

Damped and Driven Breathers and Metastability

Thermo-mechanical Transport in Rotor Chains

Contact Info

Product

Resources

About