Marco Frasca
Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.
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One loop field theory calculations of free energies quite often yield violations of the stability conditions associated with the thermodynamic second law. Perhaps the best known example involves the equation of state of black holes. Here, it is pointed out that the Casimir force between two parallel conducting plates also violates a thermodynamic stability condition normally associated with the second law of thermodynamics.
Many-body resonances in the avalanche instability of many-body localization
本文研究多体局域化系统的雪崩热化失稳机制，发现雪崩主要通过闭合系统稀有近共振本征态间的强多体共振进行扩散，揭示了多体共振与雪崩间的详细联系。
Kelly and Leff demonstrated and discussed formal and conceptual similarities between basic thermodynamic formulas for the classical ideal gas and black body photon gas. Leff pointed out that thermodynamic formulas for the photon gas cannot be deduced completely by thermodynamic methods since these formulas hold two characteristic parameters, {\it r} and {\it b}, whose accurate values can be obtained exclusively by accurate methods of the quantum statistics (by explicit use of the Planck's or Bose-Einstein distribution). In this work we prove that the complete quantum thermodynamics of the blac…
We study the statistics of the work done, the fluctuation relations and the irreversible entropy production in a quantum many-body system subject to the sudden quench of a control parameter. By treating the quench as a thermodynamic transformation we show that the emergence of irreversibility in the nonequilibrium dynamics of closed many-body quantum systems can be accurately characterized. We demonstrate our ideas by considering a transverse quantum Ising model that is taken out of equilibrium by the instantaneous switching of the transverse field.
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. In contrast, here we need only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. More precisely, we show that given a single copy of any athermal quantum state we may extract a maximal a…
Experimental Verification of Many-Body Entanglement Using Thermodynamic Quantities
本文提出利用全局与局域可提取功之差作为热力学判据，在核磁共振平台上对多达10个量子比特的含噪纠缠态进行实验认证，并扩展至状态信息未知的多体系统。
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequ…
Many-body adiabatic passage: Instability, chaos, and quantum classical correspondence
本文研究Bose-Hubbard链中类STIRAP绝热通道方案，揭示相互作用和纠缠导致的低维与高维混沌，并通过平均场、截断Wigner和全量子模拟验证量子经典对应关系。
We demonstrate the effectiveness of quantum optimal control techniques in harnessing irreversibility generated by non-equilibrium processes, implemented in unitarily evolving quantum many-body systems. We address the dynamics of a finite-size quantum Ising model subjected to finite-time transformations, which unavoidably generate irreversibility. We show that work can be generated through such transformation by means of optimal controlled quenches, while quenching the degree of irreversibility to very low values, thus boosting the efficiency of the process and paving the way to a fully control…
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays: we consider a variety of interaction (from non-interacting to strongly correlated) and dynamical (from sudden quench to quasi-adiabatic) regimes, and draw some general conclusions in relation to work extraction and entropy production. As treatment of many-body interacting systems …
For a quantum (many-body) system with dynamical symmetry described by a given Lie group, we study the trace of exponential operators with complex coefficients in one of the irreducible subspaces in terms of the boson realization. By using this approach, for compact groups, we obtain the result of the trace that is consistent with the well-known Weyl character formula. For non-compact groups (with SU(1,1) as an application), convergent condition of the trace is also obtained. This approach may be a powerful tool to study the thermodynamics of quantum (many-body) systems in equilibrium state or …
We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body forces. We show, furthermore, that those two cases (and their multi species generalizations) are the only non-relativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well-known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the lat…
In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show…
We study the functioning of a three-level thermal machine when acting on a many-qubit system, the entire system being placed in an electromagnetic field in a stationary out-of-thermal-equilibrium configuration. This realistic setup stands in between the two so-far explored cases of single-qubit and macroscopic object targets, providing information on the scaling with system size of purely quantum properties in thermodynamic contexts. We show that, thanks to the presence of robust correlations among the qubits induced by the field, thermodynamic tasks can be delivered by the machine both locall…
We prove that for a single-component many-body system at zero temperature the inequality $E_{\rm int} \leq\, P\,V$ holds, where $E_{\rm int}$ is the interaction energy, $P$ is pressure and $V$ is volume. This inequality is proven under rather general assumptions with the use of Anderson-type bound relating ground state energies of systems with different numbers of particles. We also consider adding impurity particles to the system and derive inequalities on the chemical potential of the impurity and binding energy of the bound state of two impurities.
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.
Local memory - the ability to extract information from a subsystem about its initial state - is a central feature of many-body localization. We introduce, investigate, and compare several information-theoretic quantifications of memory and discover a hierarchical relationship among them. We also find that while the Holevo quantity is the most complete quantifier of memory, vastly outperforming the imbalance, its decohered counterpart is significantly better at capturing the critical properties of the many-body localization transition at small system sizes. This motivates our suggestion that on…
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes -- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to t…
We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism, i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a…
Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier \etal, Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose-Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of s…
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same th…
Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
本文提出谱隙表达式，并基于对 simple update 方法的小幅修改实现轻量级张量网络计算，在二维和三维横场 Ising 模型上验证了其与微扰理论结果的一致性。
Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We es…
Technological and scientific advances have given rise to an era in which coherent quantum-mechanical phenomena can be probed and experimentally-realised over unprecedented timescales in condensed matter physics. In turn, scientific interest in non-equilibrium dynamics and irreversibility signatures of thermodynamics has taken place in recent decades, particularly in relation to cold-atom platforms and thermoelectric devices. In this PhD thesis I summarise some of the most important results obtained over the duration of my PhD, on the topic of thermodynamics involving interacting many-body quan…
Work Extraction Across a Thermodynamic Hierarchy in Quantum Many-Body Systems
该研究揭示量子多体系统存在热力学层级结构，熵差（表现为互信息密度）决定了扩大允许操作范围时功增益的界限，为量子功提取提供了理论依据。
Fermionic one-body entanglement as a thermodynamic resource
本文证明双模费米子态的纠缠可在开放系统热力学过程中作为真正的量子资源，完成可分态无法实现的任务，从而为费米子纠缠的操作意义提供新见解。
Thermodynamic phases in first detected return times of quantum many-body systems
研究量子多体系统首次返回时间概率分布，发现其可映射为经典自旋链配分函数的解析延拓，且衰减方式依赖于自旋链的铁磁或顺磁相，为多体量子首次探测问题提供了热力学相的理解。
We investigate the relaxation dynamics of open non-integrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibb…
Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport p…
As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in an unperturbed basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in th…
We develop a general approach for calculating the characteristic function of the work distribution of quantum many-body systems in a time-varying potential, whose many-body wave function can be cast in the Slater determinant form. Our results are applicable to a wide range of systems including an ideal gas of spinless fermions in one dimension (1D), the Tonks-Girardeau (TG) gas of hard-core bosons, as well as a 1D gas of hard-core anyons. In order to illustrate the utility of our approach, we focus on the TG gas confined to an arbitrary time-dependent trapping potential. In particular, we use …
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