Bulgac-Kusnezov-Nosé-Hoover thermostats

Sergi, Alessandro; Ezra, Gregory S.

doi:10.1103/physreve.81.036705

Cited by 11 publications

(11 citation statements)

References 45 publications

(106 reference statements)

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“…In this work we have performed a thorough numerical investigation on the ergodicity of three important singlythermostatted one-dimensional systems. We employed a logistic thermostat within the context of the Density Dynamics formalism, with the corresponding equations of motion being a set of coupled time-reversible differential equations, see (7)- (9). These equations have the same structure as those of Nosé-Hoover, but they differ in the friction term, being linear in the Nosé-Hoover case and highly non-linear in our (logistic) case.…”

Section: Discussionmentioning

confidence: 99%

“…The Nosé-Hoover thermostat fails to be ergodic for a one-dimensional harmonic oscillator [2]. Therefore, various alternative schemes have been proposed to simulate a harmonic oscillator in the canonical ensemble [5][6][7][8][9][10], some of which seem to be ergodic, in the sense that they pass a series of different numerical tests designed to detect this property. Among the ergodic schemes, the "0532" thermostat is the only one that requires the addition of a single thermostatting force [10] (see also the discussion in [11]).…”

Section: Introductionmentioning

confidence: 99%

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Ergodicity of One-dimensional Systems Coupled to the Logistic Thermostat

Tapias¹,

Bravetti²,

Sanders³

2017

CMST

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Abstract:We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum with respect to initial conditions; the absence of visual "holes" in two-dimensional Poincaré sections; the agreement between the histograms in each variable and the theoretical marginal distributions; and the convergence of the global joint distribution to the theoretical one, as measured by the Hellinger distance. Taking a large number of random initial conditions, for certain parameter values of the thermostat we find no indication of regular trajectories and show that the time distribution converges to the ensemble one for an arbitrarily long trajectory for all the systems considered. Our results thus provide a robust numerical indication that the logistic thermostat can serve as a single one-parameter thermostat for stiff one-dimensional systems.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ergodicity of One-dimensional Systems Coupled to the Logistic Thermostat

Tapias¹,

Bravetti²,

Sanders³

2017

CMST

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“…an approach already tried by Sergi and Ezra in 2001 [13]. A slight variation of the Sergi-Ezra-Patra-Bhattacharya thermostat takes into account Bulgac and Kusnezov's observation that cubic terms favor ergodicity:…”

Section: Joint Control Of Coordinates and Velocitiesmentioning

confidence: 99%

Singly-Thermostated Ergodicity in Gibbs’ Canonical Ensemble and the 2016 Ian Snook Prize

Hoover¹,

Hoover²

2016

CMST

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For a harmonic oscillator, Nosé's single-thermostat approach to simulating Gibbs' canonical ensemble with dynamics samples only a small fraction of the phase space. Nosé's approach has been improved in a series of three steps:[1] several two-thermostat sets of motion equations have been found which cover the complete phase space in an ergodic fashion; [2] sets of single-thermostat motion equations, exerting "weak control" over both forces and momenta, have been shown to be ergodic; and [3] sets of single-thermostat motion equations exerting weak control over two velocity moments provide ergodic phase-space sampling for the oscillator and for the rigid pendulum, but not for the quartic oscillator or for the Mexican Hat potential. The missing fourth step, motion equations providing ergodic sampling for anharmonic potentials requires a further advance. The 2016 Ian Snook Prize will be awarded to the author(s) of the most interesting original submission addressing the problem of finding ergodic algorithms for Gibbs' canonical ensemble using a single thermostat.

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“…Since our final aim is to implement the thermostat in quantum-classical dynamics, in order to simulate a thermal environment interacting with a quantum system, the NHP thermostat has the nice feature of generating a thermal bath by means of the smallest possible number of degrees of freedom. In this work, we adopt the time-reversible measurepreserving algorithms introduced by Ezra [22] (and recently applied to various constant-temperature equations of motion [23]) and derive an integrator for the classical NHP thermostat. The standard test for a non-Hamiltonian thermostat is a stiff harmonic oscillator, with potential V (R) = (K /2)R 2 .…”

Section: Introductionmentioning

confidence: 99%