de Haas-van Alphen oscillation spectrum is studied for an idealized two-dimensional Fermi liquid with two parabolic bands in the case of canonical (fixed number of quasiparticles) and grand canonical (fixed chemical potential) ensembles. As already reported in the literature, oscillations of the chemical potential in magnetic field yield frequency combinations that are forbidden in the framework of the semiclassical theory. Exact analytical calculation of the Fourier components is derived at zero temperature and an asymptotic expansion is given for the high temperature and low magnetic field range. A good agreement is obtained between analytical formulae and numerical computations.
A formula for potential U of the He-4--He-4 interaction in the liquid state is obtained by the direct electromagnetic computation as a function of the interatomic distance R. The potential decreases exponentially at large R. The further development and application of the result are discussed.
We study a model for an argon-like fluid parameterised in terms of a hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behaviour of the model is obtained from the thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) of Hoye and Stell, the solution of which lends itself particularly well to a pair potential of this form. The predictions for the critical point and the coexistence curve are compared to new high resolution simulation data and to other liquid-state theories, including the hierarchical reference theory (HRT) of Parola and Reatto. Both SCOZA and HRT deliver results that are considerably more accurate than standard integral-equation approaches. Among t
We study work extraction processes mediated by finite-time interactions with an ambient bath -- emph{partial thermalizations} -- as continuous time Markov processes for two-level systems. Such a stochastic process results in fluctuations in the amount of work that can be extracted and is characterized by the rate at which the system parameters are driven in addition to the rate of thermalization with the bath. We analyze the distribution of work for the case where the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and lower bound for the variance of work showing that such processes cannot be fluctuation-free in general. We also observe that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynskis fluctuation-dissipation relation for systems initially in equilibrium. Finally, we analyse work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations and obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.
Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT-isochrons.
J.-Y. Fortin
,E. Perez
,A. Audouard
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(2004)
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"Analytical treatment of the dHvA frequency combinations due to chemical potential oscillations in an idealized two-band Fermi liquid"
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Jean-Yves Fortin P.
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