arXiv subjects

M. F. Gelin

Publications and source records attributed to M. F. Gelin.

15 recordsLinked to original sources

arXiv2024

Hamiltonian non-Hermicity: accurate dynamics with the multiple Davydov D$_2$ Ansätze

We examine the applicability of the numerically accurate method of time dependent variation with multiple Davydov Ansatze (mDA) to non-Hermitian systems. Three systems of interest includes: a non-Hermitian system of dissipative Landau-Zener transitions, a non-Hermitian, multimode Jaynes-Cummings model, and a dissipative Holstein-Tavis-Cummings model, where complex many-body dynamics are accurately captured by the mDA method. Our findings highlight the versatility of the mDA as a powerful numerical tool for investigating complex many-body non-Hermitian systems, which can be extended to explore diverse phenomena such as skin effects, excited-state dynamics, and spectral topology in the non-Hermitian field.

quant-ph↗

arXiv2015

One-dimensional transport in hybrid metal-semiconductor nanotube systems

We develop an electron transport theory for the hybrid system of a semiconducting carbon nanotube that encapsulates a one-atom-thick metallic wire. The theory predicts Fano resonances in electron transport through the system, whereby the interaction of electrons on the wire with nanotube plasmon generated near-fields blocks some of the wire transmission channels to open up the new coherent plasmon-mediated channel in the nanotube forbidden gap outside the wire transmission band. Such a channel makes the entire hybrid system transparent in the energy domain where neither wire, nor nanotube is indivudually transparent. This effect can be used to manipulate by the electron charge transfer in hybrid nanodevices built on metal-semiconductor nanotube systems.

cond-mat.mes-hall↗

arXiv2009

Asymptotic non-equilibrium steady state operators

We present a method for the calculation of asymptotic operators for nonequilibrium steady-state quantum systems. The asymptotic steady-state operator is obtained by averaging the corresponding operator in Heisenberg representation over infinitely long time. Several examples are considered to demonstrate the utility of our method. The results obtained within our approach are compared to those obtained within the Schwinger-Keldysh nonequilibrium Green's functions.

cond-mat.stat-mech↗

arXiv2009

Thermodynamics of a subensemble of a canonical ensemble

Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian, which is evaluated with respect to the overall (system+bath) equilibrium distribution. Within the second approach, the system partition function $Z_{S}$ is considered as the fundamental quantity, which is postulated to be the ratio of the overall (system+bath) and the bath partition functions, and the standard thermodynamic relation $E_{S}=-d(\ln Z_{S})/dβ$ is used to obtain the mean system energy. % ($β\equiv 1/(k_{B}T)$, $k_{B}$ is the Boltzmann constant, %and $T$ is the temperature). Employing both classical and quantum mechanical treatments, the advantages and shortcomings of the two approaches are analyzed in detail for various different systems. It is shown that already within classical mechanics both approaches predict significantly different results for thermodynamic quantities provided the system-bath interaction is not bilinear or the system of interest consists of more than a single particle. Based on the results, it is concluded that the first approach is superior.

cond-mat.stat-mech↗

arXiv2009

Calculation of semiclassical free energy differences along non-equilibrium classical trajectories

We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical Hamiltonians and trajectories, so that semiclassical partition functions can be computed, e.g., via classical molecular dynamics simulations. The Hamiltonians, however, contain additional potential-energy terms, which are proportional to $\hbar^{2}$ and are temperature-dependent. We discussed the influence of quantum interference on the nonequilibrium work and problems with unambiguous definition of the semiclassical work operator.

cond-mat.stat-mech↗

arXiv2009

Microscopic origin of the jump diffusion model

The present paper is aimed at studying the microscopic origin of the jump diffusion. Starting from the $N$-body Liouville equation and making only the assumption that molecular reorientation is overdamped, we derive and solve the new (hereafter generalized diffusion) equation. This is the most general equation which governs orientational relaxation of an equilibrium molecular ensemble in the hindered rotation limit and in the long time limit. The generalized diffusion equation is an extension of the small-angle diffusion equation beyond the impact approximation. We establish the conditions under which the generalized diffusion equation can be identified with the jump diffusion equation, and also discuss the similarities and differences between the two approaches.

cond-mat.stat-mech↗

arXiv2008

A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems

We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations and/or measurements performed on nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2008

Calculations of canonical averages from the grand canonical ensemble

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in canonical ensemble based on calculations of the expectation values in grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble.

cond-mat.stat-mech↗

arXiv2007

Directed motion and useful work from an isotropic nonequilibrium distribution

We demonstrate that a gas of classical particles trapped in an external asymmetric potential undergoes a quasiperiodic motion, if the temperature of its initial velocity distribution $T_{ne}$ differs from the equilibrium temperature, $T_{eq}$. The magnitude of the effect is determined by the value of $T_{ne}-T_{eq}$, and the direction of the motion is determined by the sign of this expression. The "loading'' and "unloading'' of the gas particles change directions of their motion, thereby creating a possibility of shuttle-like motion. The system works as a Carnot engine where the heat flow between kinetic and potential parts of the nonequilibrium distribution produces the useful work.

cond-mat.stat-mech↗

arXiv2007

Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model

In order to adequately describe molecular rotation far from equilibrium, we have generalized the J-diffusion model by allowing the rotational relaxation rate to be angular momentum dependent. The calculated nonequilibrium rotational correlation functions (CFs) are shown to decay much slower than their equilibrium counterparts, and orientational CFs of hot molecules exhibit coherent behavior, which persists for several rotational periods. As distinct from the results of standard theories, rotational and orientational CFs are found to dependent strongly on the nonequilibrium preparation of the molecular ensemble. We predict the Arrhenius energy dependence of rotational relaxation times and violation of the Hubbard relations for orientational relaxation times. The standard and generalized J-diffusion models are shown to be almost indistinguishable under equilibrium conditions. Far from equilibrium, their predictions may differ dramatically.

cond-mat.soft↗

arXiv2007

Velocity dependence of friction and Kramers relaxation rates

We study the influence of the velocity dependence of friction on the escape of a Brownian particle from the deep potential well ($E_{b} \gg k_{B}T$, $E_{b}$ is the barrier height, $k_{B}$ is the Boltzmann constant, $T$ is the bath temperature). The bath-induced relaxation is treated within the Rayleigh model (a heavy particle of mass $M$ in the bath of light particles of mass $m\ll M$) up to the terms of the order of $O(λ^{4})$, $λ^{2}=m/M\ll1$. The term $\sim 1$ is equivalent to the Fokker-Planck dissipative operator, and the term $\sim λ^{2}$ is responsible for the velocity dependence of friction. As expected, the correction to the Kramers escape rate in the overdamped limit is proportional to $λ^{2}$ and is small. The corresponding correction in the underdamped limit is proportional to $λ^{2}E_{b}/(k_{B}T)$ and is not necessarily small. We thus suggest that the effects due to the velocity-dependent friction may be of considerable importance in determining the rate of escape of an under- and moderately damped Brownian particle from a deep potential well, while they are of minor importance for an overdamped particle.

cond-mat.stat-mech↗

arXiv2006

What can be learned about molecular reorientation from single molecule polarization microscopy?

We have developed a general approach for the calculation of the single molecule polarization correlation function C(t), which delivers a correlation of the emission dichroisms at time 0 and t. The approach is model independent and valid for general asymmetric top molecules. The key dynamic quantities of our analysis are the even-rank orientational correlation functions, the weighted sum of which yields C(t). We have demonstrated that the use of non-orthogonal schemes for the detection of the single molecule polarization responses makes it possible to manipulate the weighting coefficients in the expansion of C(t). Thus valuable information about the orientational correlation functions of the rank higher than second can be extracted from C(t).

physics.chem-ph↗

arXiv2006

Angular momentum dependent friction slows down rotational relaxation under non-equilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot non-equlibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby breakdown of the linear response description [Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial non-equilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium.

cond-mat.soft↗

arXiv2006

Molecular reorientation in hydrogen-bonding liquids: through algebraic $\sim t^{-3/2}$ relaxation toward exponential decay

We present a model for the description of orientational relaxation in hydrogen-bonding liquids. The model contains two relaxation parameters which regulate the intensity and efficiency of dissipation, as well as the memory function which is responsible for the short-time relaxation effects. It is shown that the librational portion of the orientational relaxation is described by an algebraic $\sim t^{-3/2}$ contribution, on top of which more rapid and non-monotonous decays caused by the memory effects are superimposed. The long-time behavior of the orientational relaxation is exponential, although non-diffusional. It is governed by the rotational energy relaxation. We apply the model to interpret recent molecular dynamic simulations and polarization pump-probe experiments on $HOD$ in liquid $D_{2}O$ [C. J. Fecko et al, J. Chem. Phys. 122, 054506 (2005)].

cond-mat.soft↗

arXiv2005

Self-similarity of single-channel transmission for electron transport in nanowires

We demonstrate that the single-channel transmission in the resonance tunneling regime exhibits self-similarity as a function of the nanowire length and the energy of incident electrons. The self-similarity is used to design the nonlinear transformation of the nanowire length and energy which, on the basis of known values of transmission for a certain region on the energy-length plane, yields transmissions for other regions on this plane. Test calculations with a one-dimensional tight-binding model illustrate the described transformations. Density function theory based transport calculations of Na atomic wires confirm the existence of the self-similarity in the transmission.

cond-mat.mes-hall↗