Carlos Mejia Monasterio

Publications

• Particle and Energy Transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

  S. Ajisaka, F. Barra, C. Mejia-Monasterio, T. Prosen

  05/2012;

  We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic... [more] We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.

• Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

  S. Ajisaka, F. Barra, C. Mejia-Monasterio, T. Prosen

  04/2012;

  We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lind... [more] We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of non-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.
• 2.40

  Impact points

  Boundary layers in stochastic thermodynamics.

  Erik Aurell, Carlos Mejía-Monasterio, Paolo Muratore-Ginanneschi

  Physical review. E, Statistical, nonlinear, and soft matter physics. 02/2012; 85(2-1):020103.

  We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps ... [more] We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

• Boundary layers in stochastic thermodynamics

  Erik Aurell, Carlos Mejia-Monasterio, Paolo Muratore-Ginanneschi

  11/2011;

  We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps ... [more] We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give a new interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).
• 2.40

  Impact points

  Symmetry breaking between statistically equivalent, independent channels in few-channel chaotic scattering.

  C Mejía-Monasterio, G Oshanin, G Schehr

  Physical review. E, Statistical, nonlinear, and soft matter physics. 09/2011; 84(3-2):035203.

  We study the distribution function P(ω) of the random variable ω=τ_{1}/(τ_{1}+⋯+τ_{N}), where τ_{k}'s are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τ_{k}'s are independent and identically ... [more] We study the distribution function P(ω) of the random variable ω=τ_{1}/(τ_{1}+⋯+τ_{N}), where τ_{k}'s are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τ_{k}'s are independent and identically distributed random variables with a distribution Ψ(τ) characterized by a "fat" power-law intermediate tail ∼1/τ^{1+μ}, truncated by an exponential (or a log-normal) function of τ. For N=2 and N=3, we observe a surprisingly rich behavior of P(ω), revealing a breakdown of the symmetry between identical independent channels. For N=2, numerical simulations of the quasi-one-dimensional Anderson model confirm our findings.
• 7.33

  Impact points

  Optimal protocols and optimal transport in stochastic thermodynamics.

  Erik Aurell, Carlos Mejía-Monasterio, Paolo Muratore-Ginanneschi

  Physical review letters. 06/2011; 106(25):250601.

  Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (det... [more] Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

• Optimal protocols and optimal transport in stochastic thermodynamics

  Erik Aurell, Carlos Mejia-Monasterio, Paolo Muratore-Ginanneschi

  12/2010;

  Thermodynamics of small systems has become an important field of statistical physics. They are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (determinist... [more] Thermodynamics of small systems has become an important field of statistical physics. They are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in Cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a non-equilibrium transition in finite time is solved by Burgers equation of Cosmology and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

• Bias- and bath-mediated pairing of particles driven through a quiescent medium

  Carlos Mejia-Monasterio, Gleb Oshanin

  10/2010;

  A particle driven by an external force in a molecular crowding environment - a quiescent bath of other particles, makes their spatial distribution inhomogeneous: the bath particles accumulate in front of the biased particle (BP) and are depleted behind. In fact, a BP travels together with the inhomo... [more] A particle driven by an external force in a molecular crowding environment - a quiescent bath of other particles, makes their spatial distribution inhomogeneous: the bath particles accumulate in front of the biased particle (BP) and are depleted behind. In fact, a BP travels together with the inhomogeneity it creates. A natural question is what will happen with two BPs when they appear sufficiently close to each other such that the inhomogeneities around each of them start to interfere? In quest for the answer we examine here, via Monte Carlo simulations, the dynamics of two BPs in a lattice gas of bath particles. We observe that for a sufficiently dense medium, surprisingly, both BPs spend most of the time together which signifies that the interference of the microstructural inhomogeneities results in effectively attractive interactions between them. Such statistical pairing of BPs minimizes the size of the inhomogeneity and hence reduces the frictional drag force exerted on the BPs by the medium. As a result, in some configurations the center-of-mass of a pair of BPs propagates faster than a single isolated BP. These jamming-induced forces are very different from fundamental physical interactions, exist only in presence of an external force, and require the presence of a quiescent bath to mediate the interactions between the driven particles.

• Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis

  L. Delfini, S. Lepri, R. Livi, C. Mejia-Monasterio, A. Politi

  11/2009;

  We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and t... [more] We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size $\sqrt{N}$ (where $N$ is the chain length), that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system. Comment: Submitted to Journal of Physics A, Mathematical and Theoretical

• Nonequilibrium dynamics of a stochastic model of anomalous heat transport

  S. Lepri, C. Mejia-Monasterio, A. Politi

  11/2009;

  We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A:... [more] We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion. Comment: Submitted to Journal of Physics A, Mathematical and Theoretical

• Superdiffusive Heat Transport in a class of Deterministic One-Dimensional Many-Particle Lorentz gases

  Pierre Collet, Jean-Pierre Eckmann, Carlos Mejia-Monasterio

  10/2008;

  We study heat transport in a one-dimensional chain of a finite number $N$ of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper, \cite{CE08}, a spatially cont... [more] We study heat transport in a one-dimensional chain of a finite number $N$ of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper, \cite{CE08}, a spatially continuous version of this model was derived in a scaling regime where the scattering probability of the tracers is $\gamma\sim1/N$, corresponding to the Grad limit. A Boltzmann type equation describing the transport of heat was obtained. In this paper, we show numerically that the Boltzmann description obtained in \cite{CE08} is indeed a bona fide limit of the particle model. Furthermore, we also study the heat transport of the model when the scattering probability is one, corresponding to deterministic dynamics. At a coarse grained level the model behaves as a persistent random walker with a broad waiting time distribution and strong correlations associated to the deterministic scattering. We show, that, in spite of the absence of global conserved quantities, the model leads to a superdiffusive heat transport. Ref CE08 P. Collet and J. P. Eckmann. A model of heat conduction. ArXiv 0804:3025, 2008.

• Thermoelectric transport in billiard systems

  Giulio Casati, Carlos Mejia-Monasterio

  09/2008;

  We discuss the thermoelectric (TE) transport in billiard systems of interacting particles, coupled to stochastic particle reservoirs. Recently in [1], analytical exact expressions for the TE transport of noninteracting gases of polyatomic molecules were obtained, and a novel microscopic mechanism fo... [more] We discuss the thermoelectric (TE) transport in billiard systems of interacting particles, coupled to stochastic particle reservoirs. Recently in [1], analytical exact expressions for the TE transport of noninteracting gases of polyatomic molecules were obtained, and a novel microscopic mechanism for the increase of thermoelectric efficiency described. After briefly reviewing the derivation of [1], in this paper we focus on the effects that the particle-particle interaction has on the TE efficiency. We show that interaction reduces the maximal thermodynamic efficiency. However, the mechanism for the efficiency's increase towards its Carnot upper limit, described in [1], remains unaffected.

• A stochastic model of anomalous heat transport: analytical solution of the steady state

  Stefano Lepri, Carlos Mejia-Monasterio, Antonio Politi

  09/2008;

  We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate $\gamma$. The stationary equations for... [more] We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate $\gamma$. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit ($N\to\infty$). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of $\gamma$. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as $1/\sqrt{\gamma N}$. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite $N$.
• 7.33

  Impact points

  Increasing thermoelectric efficiency: a dynamical systems approach.

  Giulio Casati, Carlos Mejía-Monasterio, Tomaz Prosen

  Physical review letters. 08/2008; 101(1):016601.

  Inspired by the kinetic theory of ergodic gases and chaotic billiards, we propose a simple microscopic mechanism for the increase of thermoelectric efficiency. We consider the cross transport of particles and energy in open classical ergodic billiards. We show that, in the linear response regime, wh... [more] Inspired by the kinetic theory of ergodic gases and chaotic billiards, we propose a simple microscopic mechanism for the increase of thermoelectric efficiency. We consider the cross transport of particles and energy in open classical ergodic billiards. We show that, in the linear response regime, where we find exact expressions for all transport coefficients, the thermoelectric efficiency of ideal ergodic gases can approach the Carnot efficiency for sufficiently complex charge carrier molecules. Our results are clearly demonstrated with a simple numerical simulation of a Lorentz gas of particles with internal rotational degrees of freedom.

• Increasing thermoelectric efficiency towards the Carnot limit

  Giulio Casati, Carlos Mejia-Monasterio, Tomaz Prosen

  02/2008;

  We study the problem of thermoelectricity and propose a simple microscopic mechanism for the increase of thermoelectric efficiency. We consider the cross transport of particles and energy in open classical ergodic billiards. We show that, in the linear response regime, where we find exact expression... [more] We study the problem of thermoelectricity and propose a simple microscopic mechanism for the increase of thermoelectric efficiency. We consider the cross transport of particles and energy in open classical ergodic billiards. We show that, in the linear response regime, where we find exact expressions for all transport coefficients, the thermoelectric efficiency of ideal ergodic gases can approach Carnot efficiency for sufficiently complex charge carrier molecules. Our results are clearly demonstrated with a simple numerical simulation of a Lorentz gas of particles with internal rotational degrees of freedom.

• On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems

  Carlos Mejia-Monasterio, Lamberto Rondoni

  10/2007;

  We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modell... [more] We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in [D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate $\zL$ and of the dissipation function $\zW$, a similar relaxation regime at shorter averaging times is found. The quantity $\zW$ satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity $\zL$ appears to begin a monotonic convergence after such times. This is consistent with the fact that $\zW$ and $\zL$ differ by a total time derivative, and that the tails of the probability distribution function of $\zL$ are Gaussian.

• Heat Flow in Classical and Quantum Systems and Thermal Rectification

  Giulio Casati, Carlos Mejia-Monasterio

  10/2007;

  The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction may lead to potentially interesting applications based on the ... [more] The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction may lead to potentially interesting applications based on the possibility to control the heat flow. Indeed, different models of thermal rectifiers has been recently proposed in which heat can flow preferentially in one direction. Although these models are far away from a prototype realization, the underlying mechanisms are of very general nature and, as such, are suitable of improvement and may eventually lead to real applications. We briefly discuss the problem of heat transport in classical and quantum systems and its relation to the chaoticity of the dynamics. We then study the phenomenon of thermal rectification and briefly discuss the different types of microscopic mechanisms that lead to the rectification of heat flow.

• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories

  Carlos Mejia-Monasterio, Hannu Wichterich

  10/2007;

  We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quan... [more] We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.

• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

  Lamberto Rondoni, Carlos Mejia-Monasterio

  09/2007;

  The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic a... [more] The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.
• 7.33

  Impact points

  Magnetically induced thermal rectification.

  Giulio Casati, Carlos Mejía-Monasterio, Tomaz Prosen

  Physical review letters. 04/2007; 98(10):104302.

  We consider far from equilibrium heat transport in chaotic billiard chains with noninteracting charged particles in the presence of nonuniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the... [more] We consider far from equilibrium heat transport in chaotic billiard chains with noninteracting charged particles in the presence of nonuniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths.