Non-equilibrium effects and self-heating in single-electron Coulomb blockade devices

We present a comprehensive investigation of non-equilibrium effects and self-heating in single electron transfer devices based primarily on the Coulomb blockade effect. During an electron trapping process, a hot electron maybe deposited in a quantum dot or metal island, with an extra energy usually of the order of the Coulomb charging energy, which is much higher than the temperature in typical experiments. The hot electron may relax through three channels: tunneling back and forth to the feeding lead (or island), emitting phonons, and exciting background electrons. Depending on the magnitudes of the rates in the latter two channels relative to the device operation frequency and to each other, the system may be in one of three different regimes: equilibrium, non-equilibrium, and self-heating (partial equilibrium). In the equilibrium regime, a hot electron fully gives up its energy to phonons within a pump cycle. In the non-equilibrium regime, the relaxation is via tunneling with a distribution of characteristic rates; the approach to equilibrium goes like a power law of time (frequency) instead of an exponential. This channel is plagued completely in the continuum limit of the single-electron levels. In the self-heating regime, the hot electron thermalizes quickly with background electrons, whose temperature T_e is elevated above the lattice temperature T_ol. We have calculated the coefficient in the well-known T⁵ law of energy dissipation rate, and compared the results to experimental values for aluminum and copper islands and for a two-dimensional semiconductor quantum dot. Moreover, we have obtained different scaling relations between the electron temperature, the operation frequency and device size for various types of devices.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

Non-equilibrium behavior at a liquid-gas critical point

Second-order phase transitions in a non-equilibrium liquid-gas model with reversible mode couplings, i.e., model H for binary-fluid critical dynamics, are studied using dynamic field theory and the renormalization group. The system is driven out of equilibrium either by considering different values for the noise strengths in the Langevin equations describing the evolution of the dynamic variables (effectively placing these at different temperatures), or more generally by allowing for anisotropic noise strengths, i.e., by constraining the dynamics to be at different temperatures in d _|| - and d _⊥-dimensional subspaces, respectively. In the first, isotropic case, we find one infrared-stable and one unstable renormalization group fixed point. At the stable fixed point, detailed balance is dynamically restored, with the two noise strengths becoming asymptotically equal. The ensuing critical behavior is that of the standard equilibrium model H. At the novel unstable fixed point, the temperature ratio for the dynamic variables is renormalized to infinity, resulting in an effective decoupling between the two modes. We compute the critical exponents at this new fixed point to one-loop order. For model H with spatially anisotropic noise, we observe a critical softening only in the d _⊥-dimensional sector in wave vector space with lower noise temperature. The ensuing effective two-temperature model H does not have any stable fixed point in any physical dimension, at least to one-loop order. We obtain formal expressions for the novel critical exponents in a double expansion about the upper critical dimension d _c = 4 - d _|| and with respect to d _|| , i.e., about the equilibrium theory. Received 4 April 2002 Published online 13 August 2002     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

Determination of equilibrium composition of C x H y O z N t plasmas out of thermodynamic equilibrium

In this paper, we determine the composition of C_xH_yO_zN_t plasmas out of thermodynamic equilibrium using a more rigorous thermodynamic derivation of the Saha equation modified to two-temperature plasma system proposed by Chen et al. The calculation is made for these plasmas in pressure range 0.1-1 MPa and for electron temperature range 5 000-30 000 K. A great attention is given to the evolution of the major species such as hydrogen components (H, H₂), carbon monoxide (CO) and electrons. We compared the results obtained with our previous experimental and theoretical studies; the latter one has been carried out in equilibrium situation. We also compared our results with those given by the method based on the minimization of the Gibbs free energy widely used in the literature. Received 29 December 2000 and Received in final form 28 August 2001     

Deterministic derivation of non-equilibrium free energy theorems for natural isothermal isobaric systems

The non-equilibrium free energy theorems show how distributions of work along non-equilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching.     

The thermodynamic functions of ferroelectric and paraelectric SbSI

A first-principle method is used to calculate phonon density of states, Helmholtz free energy, internal energy, and entropy for ferroelectric and paraelectric SbSI. Theoretical phase transition temperature was obtained using the difference of the Helmholtz free energy, internal energy, and entropy term between ferroelectric and paraelectric phases on temperature. The obtained value is in reasonable agreement with the experimental second-order phase transition temperature T_c2 = 233 K.     

α-helix↔random coil phase transition: analysis of ab initio theory predictions

In the present paper we present results of calculations obtained with the use of the theoretical method described in our preceding paper [Eur. Phys. J. D, DOI: 10.1140/epjd/e2007-00328-9] and perform detail analysis of α-helix↔random coil transition in alanine polypeptides of different length. We have calculated the potential energy surfaces of polypeptides with respect to their twisting degrees of freedom and construct a parameter–free partition function of the polypeptide using the suggested method [Eur. Phys. J. D, DOI: 10.1140/epjd/e2007-00328-9]. From the build up partition function we derive various thermodynamical characteristics for alanine polypeptides of different length as a function of temperature. Thus, we analyze the temperature dependence of the heat capacity, latent heat and helicity for alanine polypeptides consisting of 21, 30, 40, 50 and 100 amino acids. Alternatively, we have obtained same thermodynamical characteristics from the use of molecular dynamics simulations and compared them with the results of the new statistical mechanics approach. The comparison proves the validity of the statistical mechanic approach and establishes its accuracy.     

Dynamical block analysis in a non-equilibrium system

We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis. This can lead to a new approach in the study of non-equilibrium phenomena. We show that with such an analysis one can obtain results on the dynamic evolution as the system evolves, consistent with those obtained from and analysis of the pair-distribution function, structure factor and excess energy. The simulations were carried out on the parallel computer of the condensed matter theory group at the University of Mainz.     

A note on thermal activation

Thermal activation is mediated by field configurations that correspond to saddle points of the energy functional. The rate of probability flow along the unstable functional directions, i.e. the activation rate, is usually obtained from the imaginary part of a suitable analytic continuation of the equilibrium free energy. In this note we provide a real-time, non-equilibrium interpretation of this imaginary part which is analogous to the real-time interpretation of the imaginary part of the one-loop effective potential in theories with symmetry breaking. We argue that in situations in which the system is strongly out of equilibrium the rate will be time dependent, and illustrate this with an example.     

Coherent transport in disordered metals out of equilibrium

We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with eV/kT, and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium. Received 13 June 2001     

Electrical and thermal studies in the commensurate incommensurate phase region of (NH4)2ZnCl4 single crystal

DC electrical conductivity for a virgin and poled annealed (NH₄)₂ZnCl₄b-axis single crystal shows a defect controlled property. A Schottky mechanism is a probable mechanism of conduction in regions of strong structural transitions. The rise of conductivity in the incommensurate and paraelectric phases is linked to an increase in discommensurations density. The activation energies (ΔE) in the three phases region were calculated. DTA measurements shows that the crystal is stable up to 200 °C and the phase transition temperatures were observed at 42, 94.8 and 137 °C. The effective activation energy (E_e) was obtained using Kissinger and Mahadevan equations. It was found to be equal to 0.49 eV. This correlates with the value obtained through DC conductivity.     

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K^?/K⁺ ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K^?/K⁺ ratio using the equilibrium theory, even though the production processes for K⁺'s and K^?'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.     

Structural, elastic and thermal properties of the compound LaNi4.5Sn0.5

The equilibrium lattice constants, cell volumes, densities of states and electron density distributions of LaNi_4.5Sn_0.5 crystal are evaluated by the density functional theory using the plane wave pseudopotential (PW-PP) method. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained from the PW-PP method, is applied to the study of thermal and vibrational effects. We have analyzed the bulk modulus of LaNi_4.5Sn_0.5 as a function of temperature up to 1000 K. The thermodynamic properties such as thermal expansion coefficients and heat capacities are also predicted using the quasi-harmonic Debye model. Significant differences in properties are observed at high temperatures and pressures. Moreover, the Debye temperatures are determined from the non-equilibrium Gibbs functions. The calculated results are in excellent agreement with the available experimental data, and compared favorably with other theoretical results.     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.     

Nonequilibrium states of driven disordered polymorphic solids

Condensed matter systems, when driven far from equilibrium, often exhibit a far more varied set of phases than their equilibrium counterparts. The existence of non-equilibrium analogs of ‘solids’ and ‘liquids’ has been demonstrated earlier in the context of models for driven disordered vortex lattices in superconductors. Here we study the effects of a structural (polymorphic) transition in a driven two-dimensional crystal placed in a quenched random background. Such a polymorphic crystal is shown to exhibit a complex sequence of unusual dynamical phases as the external drive is varied, including some which have no analog in the undriven pure system. We propose that such states should be accessible in experiments.     

Insulator-metal transition in biased finite polyyne systems

A method for the study of the electronic transport in strongly coupled electron-phonon systems is formalized and applied to a model of polyyne chains biased through metallic Au leads. We derive a stationary non equilibrium polaronic theory in the general framework of a variational formulation. The numerical procedure we propose can be readily applied if the electron-phonon interaction in the device hamiltonian can be approximated as an effective single particle electron hamiltonian. Using this approach, we predict that finite polyyne chains should manifest an insulator-metal transition driven by the non-equilibrium charging which inhibits the Peierls instability characterizing the equilibrium state.     

Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs

We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi reservoirs ?₁, ?₂, which are in thermal equilibrium at inverse temperatures β₁≠β₂. We prove that, at small coupling, the combined quantum system ?+?₁+?₂ has a unique non-equilibrium steady state (NESS) and that the approach to this NESS is exponentially fast. We show that the entropy production of the coupled system is strictly positive and relate this entropy production to the heat fluxes through the system. A part of our argument is general and deals with spectral theory of NESS. In the abstract setting of algebraic quantum statistical mechanics we introduce the new concept of the C-Liouvillean, L, and relate the NESS to zero resonance eigenfunctions of L ^*. In the specific model ?+?₁+?₂ we study the resonances of L ^* using the complex deformation technique developed previously by the authors in [JP1]. Dedicated to Jean Michel Combes on the occasion of his sixtieth birthday Received: 12 July 2001 / Accepted: 11 October 2001