Cyclic Thermodynamic Processes and Entropy Production

We study the time evolution of a periodically driven quantum-mechanical system coupled to several reservoirs of free fermions at different temperatures. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics of the coupled system on an extended Hilbert space. We show that the time-periodic state which the state of the coupled system converges to after very many periods corresponds to a zero-energy resonance of the Floquet Liouvillean. We then show that the entropy production per cycle is (strictly) positive, a property that implies Carnot's formulation of the second law of thermodynamics.     

A Robust Protocol for Entropy Measurement in Mesoscopic Circuits

Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement.     

A Bayesian Entropy Approach to Sectoral Systemic Risk Modeling

We investigate the dynamics of systemic risk of European companies using an approach that merges paradigmatic risk measures such as Marginal Expected Shortfall, CoVaR, and Delta CoVaR, with a Bayesian entropy estimation method. Our purpose is to bring to light potential spillover effects of the entropy indicator for the systemic risk measures computed on the 24 sectors that compose the STOXX 600 index. Our results show that several sectors have a high proclivity for generating spillovers. In general, the largest influences are delivered by Capital Goods, Banks, Diversified Financials, Insurance, and Real Estate. We also bring detailed evidence on the sectors that are the most pregnable to spillovers and on those that represent the main contributors of spillovers.     

计算混沌光场熵的新方法

熵是量子光场的一个重要物理量,我们给出求混沌光场对应的热态的新方法,即有序算符内的积分方法,在此基础上计算光场的熵十分简捷。     

Transition from the Kondo effect to a Coulomb blockade in an electron shuttle

We investigate the effect of the mechanical motion of a quantum dot on the transport properties of a quantum dot shuttle.Employing the equation of motion method for the nonequilibrium Green’s function,we show that the oscillation of the dot,i.e.,the time-dependent coupling between the dot’s electron and the reservoirs,can destroy the Kondo effect.With the increase in the oscillation frequency of the dot,the density of states of the quantum dot shuttle changes from the Kondo-like to a Coulomb-blockade pattern.Increasing the coupling between the dot and the electrodes may partly recover the Kondo peak in the spectrum of the density of states.Understanding of the effect of mechanical motion on the transport properties of an electron shuttle is important for the future application of nanoelectromechanical devices.     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Entropy as a measure of the noise extent in a two-level quantum feedback controlled system

By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Quantum phase transition and Coulomb blockade effect in triangular quantum dots with interdot capacitive and tunnel couplings

The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method.We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t.For small t,three dots form a local spin doublet.As t increases,due to the competition between V and t,there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet.When t is absent,the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage.While for sufficient t,the antiferromagnetic spin correlation between dots is enhanced,and the conductance is strongly suppressed for the bonding state is almost doubly occupied.     

From Rényi Entropy Power to Information Scan of Quantum States

In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.     

玻璃中的半导体量子点

介绍了玻璃中的半导体量子点。对玻璃中半导体量子点的生长过程、量子的电子态，量子尺寸效应、库仑阻塞效应及介电效应，做了比较全面的介绍。讨论了量子点的应用及发展前景。     

Measuring fluorescence to track a quantum emitter's state: a theory review

We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results.     

A Finite Partition in a Dynamical System with Entropy Depending on the Size

A finite partition X in a C*-dynamical system has the Alicki–Fannes entropy depending on the size of X so that the dynamical entropy is . Examples are given as Cuntz's canonical endomorphism, the inner automorphism Adu on the crossed product of a quantum spin chain by the shift, and the free shift.     

Scattering as a Quantum Metrology Problem: A Quantum Walk Approach

We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity and use the quantum Fisher information as a means to quantify the maximal possible accuracy in the estimation of the height of the barrier. We introduce suitable initial states of the walker and derive the reflection and transmission probabilities of the scattered state. We show that while the quantum Fisher information is affected by the width and central momentum of the initial wave packet, this dependency is weaker for the quantum signal-to-noise ratio. We also show that a dichotomic position measurement provides a nearly optimal detection scheme.     

Dynamics of Entropy Production Rate in Two Coupled Bosonic Modes Interacting with a Thermal Reservoir

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.     

量子点系统的热力学稳定性及其单粒子分布函数的性质:非零温时的情况

利用一个量子点系统热力学稳定性的要求及量子统计物理中的Klein不等式,证明了在非零温度时,该系统的单粒子分布函数对于量子点上单粒子能级而言仍然是非增的.这一结果表明,一个量子多体系统中谱函数的行为在很大程度上是由其热力学稳定性条件决定的.     

A mean field approach to Coulomb blockade for a disordered assembly of quantum dots

The Coulomb blockade (CB) in quantum dots (QDs) is by now well documented. It has been used to guide the fabrication of single electron transistors. Even the most sophisticated techniques for synthesizing QDs (e.g. MOCVD/MBE) result in an assembly in which a certain amount of disorder is inevitable. On the other hand, theoretical approaches to CB limit themselves to an analysis of a single QD. In the present work we consider two types of disorders: (i) size disorder; e.g. QDs have a distribution of sizes which could be unimodal or bimodal in nature. (ii) Potential disorder with the confining potential assuming a variety of shapes depending on growth condition and external fields. We assume a Gaussian distribution in disorder in both size and potential and employ a simplified mean field theory. To do this we rely on the scaling laws for the CB (also termed as Hubbard U) obtained for an isolated QD [1]. We analyze the distribution in the Hubbard U as a consequence of disorder and observe that Coulomb blockade is partially suppressed by the disorder. Further, the distribution in U is a skewed Gaussian with enhanced broadening.      

Entropy Production and Transports in a Conservative Multibaker Map with Energy

For a previously introduced conservative multibaker map with energy, the Gaspard–Gilbert–Dorfman entropy production of the stationary state induced by the flux boundary condition is calculated and the entropy production is shown (i) to be nonnegative, (ii) to vanish in the fine-grained limit for finite chains, (iii) to take the phenomenologically expected value in the middle of the chain and to deviate from it near the boundaries, and (iv) to reduce to the phenomenological expression in the scaling limit where the lattice site nZ and time tZ are scaled respectively as n=L X and t=L T and the limits of L + and L + are taken while keeping the diffusion coefficient D=lL /L ² constant, l being the transition rate of the model. The mass and heat transports are also studied in the scaling limit under an additional assumption that the edges of the chain are in equilibrium with different temperatures. In the linear heat transport regime, Fourier's law of heat conduction and the thermodynamic expression of the associated entropy production are obtained.