arXiv subjects

Hans C. Fogedby

Publications and source records attributed to Hans C. Fogedby.

At least 19 recordsLinked to original sources

arXiv2026

Steady state coherence in a qubit is incompatible with a quantum map

We consider the recent proposal of steady state coherences in a single qubit in the case of a composite system-bath interaction. Based on a field theoretical approach we reanalyse the issue within a Redfield description. We find that the Redfield approach in accordance with a recent proposal yields steady state coherences but also violates the properties of a quantum map yielding negative populations. The issue is resolved by applying the Lindblad equation which is in accordance with a proper quantum map. The Lindblad equation, however, also implies the absence of steady state coherence. We conclude that steady state coherence in a a qubit is incompatible with a quantum map.

quant-ph↗

arXiv2026

On the Redfield and Lindblad master equations

In a previous work we developed a field theoretical approach to open quantum systems using condensed matter methods. In the Born approximation we derived the Redfield equation on the basis of a multi-oscillator bath, a Dyson equation, a diagrammatic expansion and a quasi-particle approximation. In addition applying a rotating wave approximation we obtained the Lindblad equation describing a proper quantum map. The issue regarding the additional rotating wave approximation was left as an open problem. The present work addresses the open problem and presents new results. We identify a discrepancy in the popular and standard Redfield equation. The discrepancy is associated with the well-known fact that the Redfield equation does not represent a proper quantum map. The discrepancy is related to the diagrammatic expansion and a consistency requirement in the quasi-particle approximation. The explicit resolution of this discrepancy is obtained by imposing energy conservation on the Born level. As a result we obtain formal equivalence between the energy-conserving Redfield equation and the Lindblad equation without invoking the rotating wave approximation. We provide a detailed mapping of the field theoretical approach to the standard microscopic derivation in the theory of open quantum systems.

quant-ph↗

arXiv2024

Heat currents in qubit systems

There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e., the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born-Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.

quant-ph↗

arXiv2022

Field-theoretical approach to open quantum systems and the Lindblad equation

We develop a systematic field-theoretical approach to open quantum systems based on condensed-matter many-body methods. The time evolution of the reduced density matrix for the open quantum system is determined by a transmission matrix. Developing diagrammatic perturbation theory, invoking Wick's theorem in connection with a Caldeira-Leggett quantum oscillator environment in thermal equilibrium, the transmission matrix satisfies a Dyson equation characterized by an irreducible kernel. Unlike the Nakajima-Zwanzig and standard approaches, the Dyson equation is equivalent to a general non-Markovian master equation for the reduced density matrix, incorporating secular effects and independent of the initial preparation. The kernel is determined by a systematic diagrammatic expansion in powers of the interaction. We consider the Born approximation for the kernel. Applying a condensed-matter pole or, equivalently, a quasiparticle-type approximation, equivalent to the usual assumption of a timescale separation, we derive a master equation of the Markov type. Furthermore, imposing the rotating-wave approximation,we obtain a Markov master equation of the Lindblad form. To illustrate the method, we consider the standard example of a single qubit coupled to a thermal heat bath.

quant-ph↗

arXiv2021

Aspects of the disordered harmonic chain

We discuss the driven harmonic chain with fixed boundary conditions subject to weak coupling strength disorder. We discuss the evaluation of the Liapunov exponent in some detail expanding on the dynamical system theory approach by Levi et al. We show that including mass disorder the mass and coupling strength disorder can be combined in a renormalised mass disorder. We review the method of Dhar regarding the disorder-averaged heat current, apply the approach to the disorder-averaged large deviation function and finally comment on the validity of the Gallavotti-Cohen fluctuation theorem. The paper is also intended as an introduction to the field and includes detailed calculations.

cond-mat.stat-mech↗

arXiv2020

Heat fluctuations in equilibrium

The characteristic function for heat fluctuations in a non equilibrium system is characterised by a large deviation function whose symmetry gives rise to a fluctuation theorem. In equilibrium the large deviation function vanishes and the heat fluctuations are bounded. Here we consider the characteristic function for heat fluctuations in equilibrium, constituting a sub-leading correction to the large deviation behaviour. Modelling the system by an oscillator coupled to an explicit multi-oscillator heat reservoir we evaluate the characteristic function.

cond-mat.stat-mech↗

arXiv2018

Autonomous quantum rotator

We consider a minimal model of a quantum rotator composed of a single particle confined in an harmonic potential and driven by two temperature-biased heat reservoirs. In the case the particle potential is rendered asymmetric and rotated an angle, a finite angular momentum develops, corresponding to a directed rotary motion. At variance with the classical case, the thermal fluctuations in the baths give rise to a non-vanishing average torque contribution; this is a genuine quantum effect akin to the Casimir effect. In the steady state the heat current flowing between the two baths is systematically converted into particle rotation. We derive exact expressions for the work rate and heat currents in the case where the system is driven by an external time periodic mechanical force. We show, in agreement with previous works on classical systems, that for this choice of external manipulation protocol, the rotator cannot work either as a heat pump or as a heat engine. We finally use our exact results to extend an ab-initio quantum simulation algorithm to the out-of-equilibrium regime.

quant-ph↗

arXiv2017

A minimal model of an autonomous thermal motor

We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non- vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the Büttiker-Landauer model [1-3] for a single particle diffusing in an environment with position dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.

cond-mat.stat-mech↗

arXiv2014

Heat flow in chains driven by thermal noise

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar and in the classical regime by Saito and Dhar and Kundu et al. Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution which turn out to decay exponentially. We, moreover, consider an extension of a single particle model suggested by Derrida and Brunet and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.

cond-mat.stat-mech↗

arXiv2014

Energetics and efficiency of a molecular motor model

The energetics and efficiency of a linear molecular motor model proposed by Mogilner et al. (Phys. Lett. 237, 297 (1998)) is analyzed from an analytical point of view. The model which is based on protein friction with a track is described by coupled Langevin equations for the motion in combination with coupled master equations for the ATP hydrolysis. Here the energetics and efficiency of the motor is addressed using a many body scheme with focus on the efficiency at maximum power (EMP). It is found that the EMP is reduced from about 10 pct in a heuristic description of the motor to about 1 per mille when incorporating the full motor dynamics, owing to the strong dissipation associated with the motor action.

cond-mat.stat-mech↗

arXiv2014

Heat fluctuations and fluctuation theorems in the case of multiple reservoirs

We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry leads to a generalisation of the asymptotic fluctuation theorem for large deviations at large times. As a result the presence of multiple reservoirs influence the tails in the heat distribution. The symmetry, moreover, allows for a simple derivation of a recent exact fluctuation theorem valid at all times. Including a time dependent work protocol we also present a derivation of the integral fluctuation theorem.

cond-mat.stat-mech↗

arXiv2014

Large deviations in the alternating mass harmonic chain

We extend the work of Kannan et al. and derive the cumulant generating function for the alternating mass harmonic chain consisting of N particles and driven by heat reservoirs. The main result is a closed expression for the cumulant generating function in the thermodynamic large N limit. This expression is independent of N but depends on whether the chain consists of an even or an odd number of particles, in accordance with the results obtained by Kannan el al. for the heat current. This result is in accordance with the absence of local thermodynamic equilibrium in a linear system.

cond-mat.stat-mech↗

arXiv2011

Bound particle coupled to two thermostats

We consider a harmonically bound Brownian particle coupled to two distinct heat reservoirs at different temperatures. We show that the presence of a harmonic trap does not change the large deviation function from the case of a free Brownian particle discussed by Derrida and Brunet and Visco. Likewise, the Gallavotti-Cohen fluctuation theorem related to the entropy production at the heat sources remains in force. We support the analytical results with numerical simulations.

cond-mat.stat-mech↗

arXiv2009

Heat distribution function for motion in a general potential at low temperature

We consider the 1D motion of an overdamped Brownian particle in a general potential in the low temperature limit. We derive an explicit expression for the probability distribution for the heat transferred to the particle. We find that the local minima in the potential yield divergent side bands in the heat distribution in addition to the divergent central peak. The position of the bands are determined by the potential gaps. We, moreover, determine the tails of the heat distribution.

cond-mat.stat-mech↗

arXiv2009

Minimum action method for the Kardar-Parisi-Zhang equation

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise driven Burgers equation. The transition scenario is in accordance with recent analytical studies of the one dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.

cond-mat.stat-mech↗

arXiv2008

Patterns in the Kardar-Parisi-Zhang equation

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.

cond-mat.stat-mech↗

arXiv2007

Dynamics of DNA-breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

cond-mat.stat-mech↗

arXiv2007

Stochastic Loewner Evolution

Stochastic Loewner evolution also called Schramm Loewner evolution (abbreviated, SLE) is a rigorous tool in mathematics and statistical physics for generating and studying scale invariant or fractal random curves in two dimensions. The method is based on the older deterministic Loewner evolution introduced by Karl Loewner, who demonstrated that an arbitrary curve not crossing itself can be generated by a real function by means of a conformal transformation. In 2000 Oded Schramm extended this method and demonstrated that driving the Loewner evolution by a one-dimensional Brownian motion, the curves in the complex plane become scale invariant; the fractal dimension turns out to be determined by the strength of the Brownian motion. SLE fills a gap in our understanding of the critical properties of a variety of lattice models in their scaling limits and supplements the result obtained by means of conformal field theory. In this paper we attempt to provide a simple and heuristic discussion of some of the important aspects of SLE.

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