scholarly journals Landau theory for non-equilibrium steady states

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Camille Aron ◽  
Claudio Chamon
Keyword(s):  
Landau Theory ◽  
Mean Field ◽  
Continuous Phase ◽  
Steady States ◽  
Dissipative Systems ◽  
Driving Frequency ◽  
Periodically Driven ◽  
Single Bath ◽  
Different Temperatures ◽  
Non Equilibrium

We examine how non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.

scholarly journals Magnus Expansion Approach to Parametric Oscillator Systems in a Thermal Bath

2016 ◽  
Vol 71 (10) ◽  
pp. 921-932 ◽  
Author(s):  
Beilei Zhu ◽  
Tobias Rexin ◽  
Ludwig Mathey
Keyword(s):  
Parametric Instability ◽  
Parametric Oscillator ◽  
Dissipative Systems ◽  
Thermal Bath ◽  
Driving Frequency ◽  
Many Body ◽  
Magnus Expansion ◽  
Driven Systems ◽  
Oscillator Frequency ◽  
Periodically Driven

AbstractWe develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and in the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilisation at second order, we find that the higher orders further renormalise the oscillator frequency, and additionally create a weakly renormalised effective temperature. The renormalised oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

NON-EQUILIBRIUM TRICRITICAL BEHAVIOR IN LASERS

1991 ◽  
Vol 05 (04) ◽  
pp. 245-258
Author(s):  
MANSOUR MORTAZAVI ◽  
SURENDRA SINGH
Keyword(s):  
Phase Transitions ◽  
Landau Theory ◽  
Tricritical Point ◽  
Mean Field Theory ◽  
Mean Field ◽  
Second Order ◽  
Operating Parameters ◽  
Threshold Behavior ◽  
Tricritical Behavior ◽  
Non Equilibrium

Tricritical behavior in lasers is reviewed briefly. Threshold behavior in the laser with a saturable absorber is interpreted in terms of first- and second-order phase transitions within the framework of Landau theory (mean field). The intersection of the lines of first- and second order phase transitions in this system provides an example of a non-equilibrium tricritical point. By varying the operating parameters of a He:Ne laser with an intracavity Ne absorber it was possible to operate the laser near the tricritical point. Experimental results are compared with the predictions of mean field theory.

scholarly journals General description for nonequilibrium steady states in periodically driven dissipative quantum systems

2020 ◽  
Vol 6 (27) ◽  
pp. eabb4019 ◽  
Author(s):  
Tatsuhiko N. Ikeda ◽  
Masahiro Sato
Keyword(s):  
Quantum Physics ◽  
Broad Class ◽  
Quantum Systems ◽  
Steady States ◽  
Dissipative Systems ◽  
Nonequilibrium Steady States ◽  
General Description ◽  
Periodically Driven ◽  
Symmetry Properties ◽  
Dissipative Quantum Systems

Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.

Statistical Modeling of a Dislocation Phase-Field in Ductile Single Crystals

2001 ◽  
Vol 701 ◽  
Author(s):  
M. Koslowski ◽  
M. Ortiz ◽  
A.M. Cuitino
Keyword(s):  
Single Crystals ◽  
Finite Temperature ◽  
Mean Field ◽  
Hysteresis Loops ◽  
Field Approximation ◽  
Dissipative Systems ◽  
Mean Field Approximation ◽  
Metropolis Monte Carlo ◽  
Different Temperatures ◽  
Shear Stress Field

ABSTRACTA model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced. The theory accounts for: and arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and applied resolved shear stress field; and the dissipative in teractions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics are modeled with Metropolis Monte Carlo simulations and a mean field approximation. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication under monotonic loading and hysteresis loops under under cyclic loading. The flow stress was found to be dependent on the temperature and on the strain rate only at finite temperature.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment

2018 ◽  
Vol 54 (5) ◽  
pp. 427-444 ◽  
Author(s):  
R. D. Astumian
Keyword(s):  
Steady States ◽  
Absolute Amount ◽  
Fluctuating Environment ◽  
The Absolute ◽  
Non Equilibrium

Fluctuations favour state B = (B,B′) based on kinetic asymmetry combined with moderate dissipation rather than state A = (A,A′) in which the absolute amount of dissipation is greater but where there is no kinetic asymmetry.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Sign in / Sign up

Export Citation Format

Share Document