scholarly journals Coupled Nosé-Hoover equations of motion to implement a fluctuating heat-bath temperature

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
Ikuo Fukuda ◽  
Kei Moritsugu
Keyword(s):  
Equations Of Motion ◽  
Heat Bath ◽  
Bath Temperature

scholarly journals Temperature–Energy-space Sampling Molecular Dynamics: Deterministic, Iteration-free, and Single-replica Method utilizing Continuous Temperature System

2019 ◽  
Author(s):  
Ikuo Fukuda ◽  
Kei Moritsugu
Keyword(s):  
Molecular Dynamics ◽  
Random Walk ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Bath Temperature ◽  
Dynamical Variable ◽  
Energy Space ◽  
Enhanced Sampling ◽  
Dynamical Mechanism ◽  
Space Forms

AbstractWe developed coupled Nosé–Hoover (NH) molecular dynamics equations of motion (EOM), wherein the heat-bath temperature for the physical system (PS) fluctuates according to an arbitrary predetermined weight. The coupled NH is defined by suitably jointing the NH EOM of the PS and the NH EOM of the temperature system (TS), where the inverse heat-bath temperature β is a dynamical variable. In this study, we define a method to determine the effective weight for enhanced sampling of the PS states. The method, based on ergodic theory, is reliable, and eliminates the need for time-consuming iterative procedures and resource-consuming replica systems. The resulting TS potential in a two dimensional (β, ϵ)-space forms a valley, and the potential minimum path forms a river flowing through the valley. β oscillates around the potential minima for each energy ϵ, and the motion of β derives a motion of ϵ and receives the ϵ’s feedback, which leads to a mutual boost effect. Thus, it also provides a specific dynamical mechanism to explain the features of enhanced sampling such that the temperature-space “random walk” enhances the energy-space “random walk.” Surprisingly, these mutual dynamics between β and ϵ naturally arise from the static probability theory formalism of double density dynamics that was previously developed, where the Liouville equation with an arbitrarily given probability density function is the fundamental polestar. Numerical examples using a model system and an explicitly solvated protein system verify the reliability, simplicity, and superiority of the method.

TEMPERATURE OF NONEQUILIBRIUM LATTICE SYSTEMS

2006 ◽  
Vol 17 (12) ◽  
pp. 1703-1715 ◽  
Author(s):  
ALBERTO PETRI ◽  
M. J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Heat Bath ◽  
Bath Temperature ◽  
Total System ◽  
Local Distribution ◽  
Lattice Systems ◽  
Potts Models ◽  
Monte Carlo Dynamics ◽  
Instantaneous Temperature ◽  
System Energy

We investigate the thermal quench of Ising and Potts models via Monte Carlo dynamics. We find that the local distribution of the site-site interaction energy has the same form as in the equilibrium case, a result that allows us to define an instantaneous temperature θ during the systems relaxation. We also find that, after an undercritical quench, θ equals the heat bath temperature in a finite time, while the total system energy is still decreasing due to the coarsening process.

scholarly journals Open Quantum Dynamics Theory on the Basis of Periodical System-Bath Model for Discrete Wigner Function

2021 ◽  
Author(s):  
Yuki Iwamoto ◽  
Yoshitaka Tanimura
Keyword(s):  
Distribution Function ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Planck Equation ◽  
Mesh Size ◽  
Dynamics Simulation ◽  
Open Quantum

Abstract Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

Wave equation for dissipative motion

1991 ◽  
Vol 69 (10) ◽  
pp. 1225-1232 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Equation ◽  
Single Particle ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Heat Bath ◽  
Initial Position ◽  
Time Dependent ◽  
Reduced Form ◽  
Body System ◽  
Many Body

From a quantized many-body system a wave equation for the motion of a particle linearly coupled to a heat bath is derived. The effective Hamiltonian describing the motion of the single particle is explicitly time dependent, and for a quadratic potential, has a simple dependence on the initial position and momentum of the particle. For the case of dissipative harmonic motion, a time-dependent wave equation is derived and the ground-state wave function is determined. It is also shown that if the equations of motion for the many-body system is Galilean invariant, the reduced form of equation of motion for the single particle is not. However a generalized form of transformation for the position and momentum operators, to a coordinate system moving with constant velocity, is obtained, which reduces to the Galilean transformation when the coupling to the dissipative system is turned off.

scholarly journals Markovian Dynamics of Josephson Parametric Amplification

2017 ◽  
Vol 15 ◽  
pp. 131-140 ◽  
Author(s):  
Waldemar Kaiser ◽  
Michael Haider ◽  
Johannes A. Russer ◽  
Peter Russer ◽  
Christian Jirauschek
Keyword(s):  
Josephson Junction ◽  
Classical Model ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Parametric Amplifier ◽  
Coupling Constants ◽  
Quantum Limit ◽  
Main Element ◽  
Actual State ◽  
Noise Power

Abstract. In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.

Hamilton's principal function for the Brownian motion of a particle and the Schrödinger–Langevin equation

1978 ◽  
Vol 56 (3) ◽  
pp. 311-320 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Heat Bath ◽  
Linear Wave ◽  
Many Body ◽  
Formal Similarity ◽  
Linear Wave Equation ◽  
Frictional Forces

The Brownian motion of a particle coupled to a heat bath can be derived from an exactly solvable many-body system. This motion is governed by the Langevin equation in Newtonian mechanics, and by an operator equation formally identical to the Langevin equation when the system composed of the particle plus the heat bath is quantized. To get this formal similarity between the classical and the quantal equations of motion of the particle, the classical dissipative system is formulated in terms of a modified Hamilton–Jacobi equation and is then quantized using the Schrödinger method. The result is identical with the Schrödinger–Langevin equation that has been obtained by quantizing the entire system and then isolating the motion of the particle. The non-linear wave equation describing the motion of a particle subject to conservative and time-dependent forces as well as frictional forces has been applied to the problems of motion of a wave-packet, and of the scattering and trapping of heavy-ions.

SOME DYNAMICAL PROPERTIES OF THE ISING FERROMAGNET

1967 ◽  
Vol 45 (6) ◽  
pp. 2091-2111 ◽  
Author(s):  
Noboru Matsudaira
Keyword(s):  
Correlation Functions ◽  
Equations Of Motion ◽  
Pair Correlation ◽  
Linear Chain ◽  
Heat Bath ◽  
Spin Correlation ◽  
Square Lattice ◽  
Two Dimensional ◽  
The Many ◽  
Sums Of Products

Time-dependent statistics of the Ising model proposed by Glauber for the one-dimensional chain are extended to the example of a two-dimensional square lattice. Each spin is assumed to change its state through the interaction with a heat bath. The equations of motion for both the single spin and the spin correlation functions are solved approximately by using a decoupling procedure where the many-body correlation functions are taken as sums of products of pair correlation functions. As a special case, our theory allows the approximate calculation of the equilibrium properties of the system and it turns out that, in this case, our result is an improvement over the Bethe approximation. Both the frequency-dependent magnetic susceptibility and the decay of the magnetic moment to the equilibrium state are calculated above and below the Curie temperature. The fluctuation–dissipation theorem developed by Glauber for the linear chain is shown to hold in the two-dimensional case also.

scholarly journals Optomechanical oscillator controlled by variation in its heat bath temperature

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Michal Kolář ◽  
Artem Ryabov ◽  
Radim Filip
Keyword(s):  
Heat Bath ◽  
Bath Temperature

scholarly journals Mathieu-state reordering in periodic thermodynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Onno R. Diermann
Keyword(s):  
Ground State ◽  
Anharmonic Oscillator ◽  
Heat Bath ◽  
Bath Temperature ◽  
Model System ◽  
Ideal Model ◽  
Periodically Driven ◽  
Quantum Resonances ◽  
Driven System ◽  
Ideal Model System

Abstract A periodically driven, moderately anharmonic oscillator constitutes an ideal model system for investigating quantum resonances, which are amenable to a quantum pendulum approximation. In the present paper, I study the quasi-stationary Floquet-state occupation probabilities which emerge when such a resonantly driven system is coupled to a heat bath. It is demonstrated that the Floquet state which is associated with the ground state of the pendulum turns into an effective ground state, carrying the highest population in the strong-driving regime. Moreover, the population of this effective Floquet ground state can even exceed that of the undriven system’s true ground state at the same bath temperature. These effects can be optimized by suitably engineering the properties of the bath.

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