Temperature fluctuations in mesoscopic systems.

In the mesoscopic regime, the MOS device performance is affected by gate‐induced quantization effects leading to a loss of transconductance and threshold voltage shift and gate leakage tunnelling currents degrading the overall device performance. We discuss the expected impact of quantum effects in highly down scaled CMOS circuits. Based on 1‐d numerical simulations for transport in mesoscopic systems, we set up Spice circuit models. The Spice models rebuild the influence of quantum effects; and the functionality of classical circuit concepts can be ‘tested’ in their robustness against these effects. A few circuit examples will be given. Copyright © 2005 John Wiley & Sons, Ltd.

Passivity is a fundamental concept in thermodynamics that demands a quantum system’s energy cannot be lowered by any reversible, unitary process acting on the system. In the limit of many such systems, passivity leads in turn to the concept of complete passivity, thermal states and the emergence of a thermodynamic temperature. Here we only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. Indeed, we show that given a single copy of any athermal quantum state, an optimal amount of energy can be extracted from it when we utilise a machine that operates in a reversible cycle. This means that for individual systems, the only form of passivity that is stable under general reversible processes is complete passivity, and thus provides a physically motivated identification of thermal states when we are not operating in the thermodynamic limit.

The effect of spin-orbit (SO) scattering in disordered mesoscopic systems is studied. In one dimension it is shown that any spin-independent thermodynamic or transport quantity can be expressed in terms of the same quantity in the absence of SO scattering, but with an effective magnetic flux. This leads to universal SO reduction factors of the harmonics. In particular, the conductance and its fluctuations are interrelated, within and beyond weak-localization theory. Generalizations to higher dimensions are discussed.

In spite of comprehensive studies to clarify a variety of interesting phenomena of spin glasses, their understanding has been insufficiently established. To overcome such a problem, fabrication of a mesoscopic spin glass system, whose dynamics can be observed over the entire range to the equilibrium, is useful. In this review the challenges of research that has been performed up to now in this direction and our recent related studies are introduced. We have established to study the spin glass behaviour in terms of droplet picture using nanofabricated mesoscopic samples to some extent, but some problems that should be clarified have been left. Finally, the direction of some new studies is proposed to solve the problems.

We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to alternative bounds for the performance of engines. Our findings show that those limitations in control render it, in general, impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency or finite work per particle. We focus on the one-dimensional Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the antiferromagnetic case improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.

ABSTRACTWe present an efficient method to obtain bulk isothermal compressibilities () and Kirkwood–Buff (KB) integrals of single- and multicomponent liquids using fluctuations of the number of molecules obtained from small-sized molecular dynamics simulations. We write finite-size versions of the Ornstein–Zernike and the KB integral equations and include there finite size effects related to the statistical ensemble and the finite integration volumes required in computer simulations. Consequently, we obtain analytical expressions connecting and the KB integrals in the thermodynamic limit (TL) with density fluctuations in the simulated system. We validate the method by calculating various thermodynamic quantities, including the chemical potentials of SPC/E water as a function of the density, and of aqueous urea solutions as a function of the mole fraction. The reported results are in excellent agreement with calculations obtained by using the best computational methods available, thus validating the method as a tool to compute the chemical potentials of dense molecular liquids and mixtures. Furthermore, the present method identifies conditions in which computer simulations can be effectively considered in the TL.

Finite-size effects in the magnetization of periodic mesoscopic systems

We extend the effective field theory treatment of the thermodynamics of small compactified black holes to the case of charged black holes. The relevant thermodynamic quantities are computed to second order in the parameter \lambda\sim(r_0/L)^(d-3). We discuss how the addition of charge to a caged black hole may delay the phase transition to a black string. In the extremal limit, we construct an exact black hole solution which serves as a check for our perturbative results. Finite size effects are also included through higher order operators in the worldline action. We calculate how the thermodynamic quantities are modified in the presence of these operators, and show they enter beyond order \lambda^2 as in the uncharged case. Finally, we use the exact solution to constrain the Wilson coefficients of the finite size operators in the extremal limit.

A major goal of the semiclassical theory is to understand and treat a quantum system in the regime of large quantum numbers using information from its classical limit. In this framework, quantum phenomena are addressed through a path integral perspective, i.e. the weighted interference of phases accumulated along classical trajectories. While this formalism has been successful in explaining interference phenomena, for instance, in mesoscopic single-particle quantum systems, the recent extension of the semiclassical theory allows now also the treatment of interacting quantum many-body systems. This thesis aims to contribute to these ongoing efforts to apply semiclassical techniques to quantum many-body systems. It is focused on bosonic quantum many-body systems, where the thermodynamic limit of a large number of particles represents an alternative version of a semiclassical limit. Within the derivation of the corresponding semiclassical theory, mean-field equations, i.e. effective nonlinear wave equations describing the matter wave, re-emerge as Hamilton's equations of motion of an abstract Hamilton function, defining the above thermodynamic limit as the classical limit. Within this thesis, two different topics are studied. The first one deals with the so-called “Out-of-Time-Order Correlator” (OTOC), the expectation value of the squared commutator of two local operators at different times. The OTOC provides a direct probe for the presence of chaos in the classical limit (if any) of a quantum many-body system. This is based on that for short times the OTOC directly relates to the stability of classical solutions upon changes in their initial conditions. One of the defining properties of chaos is that this stability displays an exponential growth, with the rate called the classical Lyapunov exponent. Immediately, this implies an exponential growth of the OTOC for short times, from which the Lyapunov exponent can be extracted. For later times, one observes a saturation of the OTOC as a consequence of unitary quantum time evolution. The Ehrenfest time, the time scale which marks the onset of quantum interference, separates these different dynamical behaviors. In this thesis a thorough understanding of the concept of chaos in the classical limit of quantum many-body systems is provided, and with that the underlying interference mechanisms involved in the early exponential growth and the later saturation of OTOCs are identified. It is found that the pre-Ehrenfest time exponential growth is given through the interference of multiple contributions, all of them essentially following only a single solution of mean-field equations. Conversely the post-Ehrenfest time behavior stems from the contributions of fundamentally different mean-field solutions, which display correlated dynamics only for a limited amount of time, of the order of Ehrenfest time. The second topic covered in this thesis deals with the coherent transport of cold bosonic atoms through an Aharonov-Bohm ring structure. This setup consists of two semi-infinite wave guides attached on the opposite sides of a wave guide ring which is pierced by a synthetic gauge field. Within the ring, the atoms are further subject to both a weak disorder potential and particle-particle interaction. In the non-interacting case, the disorder-averaged transmission probability as a function of the encircled flux displays the well-known Al'tshuler-Aronov-Spivak (AAS) oscillations, i.e. oscillations with a frequency twice as large as Aharonov-Bohm oscillations. This thesis provides further insight into the influence of a weak particle-particle interaction on AAS oscillations, for which numerical results predict an interaction-based inversion of peaks. Here, using semiclassical techniques to solve the corresponding mean-field problem, this inversion is successfully reproduced, and a first indicator of the relevant mechanism leading to the inversion is found through contributions of self-averaging scattering path constellations.

Confinement breaks the translational symmetry of materials, making all thermodynamic and kinetic quantities functions of position. Such symmetry breaking can be used to obtain configurations that are not otherwise accessible in the bulk. Here, we use computer simulations to explore the effect of substrate-liquid interactions on thermodynamic and kinetic anisotropies induced by a solid substrate. We consider n-octane nano-films that are in contact with substrates with varying degrees of attraction, parameterized by an interaction parameter ϵS. Complete freezing of octane nano-films is observed at low temperatures, irrespective of ϵS, while at intermediate temperatures, a frozen monolayer emerges at solid-liquid and vapor-liquid interfaces. By carefully inspecting the profiles of translational and orientational relaxation times, we confirm that the translational and orientational degrees of freedom are decoupled at these frozen monolayers. At sufficiently high temperatures, however, free interfaces and solid-liquid interfaces close to loose (low-ϵS) substrates undergo "pre-freezing," characterized by mild peaks in several thermodynamic quantities. Two distinct dynamic regimes are observed at solid-liquid interfaces. The dynamics is accelerated in the vicinity of loose substrates, while sticky (high-ϵS) substrates decelerate dynamics, sometimes by as much as two orders of magnitude. These two distinct dynamical regimes have been previously reported by Haji-Akbari and Debenedetti [J. Chem. Phys. 141, 024506 (2014)] for a model atomic glass-forming liquid. We also confirm the existence of two correlations-proposed in the above-mentioned work-in solid-liquid subsurface regions of octane thin films, i.e., a correlation between atomic density and normal stress, and between atomic translational relaxation time and lateral stress. Finally, we inspect the ability of different regions of an octane film to explore the potential energy landscape by performing inherent structure calculations, and observe no noticeable difference between the free surface and the bulk in efficiently exploring the potential energy landscape. This is unlike the films of model atomic glass formers that tend to sample their respective landscape more efficiently at free surfaces. We discuss the implications of this finding to the ability of octane-and other n-alkanes-to form ultrastable glasses.

A continuous one-dimensional map with period three includes all periods. This raises the following question: Can we obtain any types of periodic orbits solely by learning three data points? In this paper, we report the answer to be yes. Considering a random neural network in its thermodynamic limit, we first show that almost all learned periods are unstable, and each network has its own characteristic attractors (which can even be untrained ones). The latently acquired dynamics, which are unstable within the trained network, serve as a foundation for the diversity of characteristic attractors and may even lead to the emergence of attractors of all periods after learning. When the neural network interpolation is quadratic, a universal post-learning bifurcation scenario appears, which is consistent with a topological conjugacy between the trained network and the classical logistic map. In addition to universality, we explore specific properties of certain networks, including the singular behavior of the scale of weight at the infinite limit, the finite-size effects, and the symmetry in learning period three.

The mechanical foundation of heat is still an important and unresolved 问题 in fundamental physics. In this paper, we systematically study the emergent deterministic descriptions of stochastic motions in the continuous space-time (macroscopic) limit, where a Liouville kinematic equation and a Hamilton-Jacobi equation (HJE) for the evolution of an entropy function are presented. As a characterization of the exponentially small infinitesimal, the HJE provides an energetic description of the kinematic equation. Most importantly, we find that the Legendre transform of the kinetic energy in the Hamiltonian of the HJE equals the macroscopic-limit heat exchange rate in the stochastic thermodynamics, leading to the fact that heat and kinetic energy are dual descriptions for the same phenomenon, based on which we propose the concept of thermokinetic energy in this paper.

Digital and mechatronic methods, paired with artificial intelligence and machine learning, are transformative technologies in behavioral science and biology. The central element of the most important pollinator species-honey bees-is the colony's queen. Because honey bee self-regulation is complex and studying queens in their natural colony context is difficult, the behavioral strategies of these organisms have not been widely studied. We created an autonomous robotic observation and behavioral analysis system aimed at continuous observation of the queen and her interactions with worker bees and comb cells, generating behavioral datasets of exceptional length and quality. Key behavioral metrics of the queen and her social embedding within the colony were gathered using our robotic system. Data were collected continuously for 24 hours a day over a period of 30 days, demonstrating our system's capability to extract key behavioral metrics at microscopic, mesoscopic, and macroscopic system levels. Additionally, interactions among the queen, worker bees, and brood were observed and quantified. Long-term continuous observations performed by the robot yielded large amounts of high-definition video data that are beyond the observation capabilities of humans or stationary cameras. Our robotic system can enable a deeper understanding of the innermost mechanisms of honey bees' swarm-intelligent self-regulation. Moreover, it offers the possibility to study other social insect colonies, biocoenoses, and ecosystems in an automated manner. Social insects are keystone species in all terrestrial ecosystems; thus, developing a better understanding of their behaviors will be invaluable for the protection and even the restoration of our fragile ecosystems globally.

Cortical activity in awake animals manifests highly complex behaviour [1]. It is during this regime that the main computational tasks are performed and no model is yet able to explain how this complex dynamics is exploited to provide a fast and accurate information processing. However, many efforts have been devoted to the study of how such activity emerges. Balanced networks have been introduced as a possible model to generate dynamical states similar to the biological ones [2]. The stability of such states was studied for current-based Integrate-And-Fire (IAF) neurons with respect to external input and excitatory-inhibitory synaptic strength ratio [3]. In particular, stable asynchronous irregular (AI) states with a relatively low level of activity have been obtained. Recently, AI states have been observed in balanced networks of conductance-based IAF neurons with self-sustained activity [4]. However, no simple description of the network activity dynamics has been developed yet. First-order mean-field approximation fails to describe these networks because of their inherent dynamics which rely dramatically on activity fluctuations. Moreover, the thermodynamic limit is usually performed for randomly connected networks despite the lack of biological relevance. We introduce here a new framework in which network dynamics as well as inherent neuron behaviour is taken into account. We aim to obtain a reduced description of mesoscopic balanced networks where finite size effects are not neglected. The model is intended to describe AI states far from critical boundaries where long-term behaviours appear. Furthermore, we set the spatial and temporal scales of the model by using biological data. Using the master equation formalism, we derive a second-order mean-field set of ordinary differential equations. The transition matrix necessary in the master equation context is computed based on the Fokker-Plank approach. Conductance-based as well as current-based IAF neurons are constructed. The kernel of this formalism lays in the way activity micro-fluctuations are modelled. We discuss different possibilities and considerations in regard to this question. This model provides at the same time an extracellular and a sub-threshold description of finite size neuron networks. Once the couplings will be adjusted, it will be possible to build a large-scale model of cortical area with specific architectures, where the fundamental unit is the randomly connected network. We further discuss the possibility to compare large-scale behaviour observed in voltage-sensitive dyes experiments with our model.

We investigate localization properties of one-dimensional electronic systems with long-range correlated disorders characterized by a power-law spectral density. An abrupt change from extended to gradon states is found to occur in individual samples independently of system sizes. This abrupt change differs from the ordinary Anderson transition in the sense that the former accompanies strong sample fluctuations that remain significant even in the thermodynamic limit. We further observe that sample-averaged quantities such as the inverse participation ratio and the level-spacing distribution exhibit nontrivial crossover behaviors from extended states to gradon states.