Langevin Equation for Particle in Thermal Photon Bath
Z. Haba, H. Kleinert
描述带电粒子在光子热浴中运动的前向-后向路径积分用Langevin型方程的解表示。讨论了求解该方程的近似方法。
The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed.
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In traditional open quantum systems, the baths are usually traced out so that only the system information is left in the equations of motion. However, recent studies reveal that using only the system degrees of freedom can be insufficient. In this work, we develop a stochastic c-number Langevin equation method which can conveniently access the bath information. In our method, the studied quantities are the expectation values of operators which can contain both system operators and bath operators. The dynamics of the operators of interest is formally divided into separate system and bath parts,…
We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and study its dynamics in the Markovian limit using the Ohmic bath model. We extend our analysis to the Drude bath with a finite memory. We study the time evolution of the expectation values of the magnetic moments. The spin auto-correlation functions exhibit a damped oscillatory behaviour with the randomization time being determined by the damping rate and also the memory time for the Drude bath model. We also analyse the spin response function of the system for the Ohmic bath model. Our results are c…
Quantum emitter interacting with a dispersive dielectric object: a model based on the modified Langevin noise formalism
本文在宏观量子电动力学框架下，用修正朗之万噪声形式主义建模量子发射器与有限色散介质物体的相互作用，揭示其耦合的两个玻色库特性及等效单玻色库条件，为相关系统动力学研究提供基础。
We analyze a system coupled to a bath of independent harmonic oscillators. We transform the bath in chain structure by solving an inverse eigenvalue problem. We solve the equations of motion for the collective variables defined by this transformation, and we derive the exact dynamics for an harmonic oscillator in terms of the microscopic motion of the environmental modes. We compare this approach to the well-known Generalized Langevin Equation and we show that our dynamics satisfies this equation.
Quantum-Liouville and Langevin Equations for Gravitational Radiation Damping
从向前-向后的路径积分，我们推导出重力子热浴中大质量量子物体发射和吸收重力子的主方程。这样的方程可以描述致密恒星的坍缩现象。我们还提出了一个有用的近似朗之万方程这样的系统。
The Generalized Schrödinger-Langevin equation
在这项工作中，我们得到了一个推广的所谓的薛定谔朗之万或Kostin方程的布朗粒子与热浴相互作用。这种推广是基于一个非线性相互作用模型，提供了一个状态相关的耗散过程，表现出乘性噪声。两个简单的应用程序的测量过程中，然后分析，连续和弱测量的量子玻姆轨迹形式主义。最后，还证明了在量子引力的某些研究中出现的广义不确定原理也可以用这个广义方程来表示
Fokker-Planck and Langevin Equations from Forward--Backward Path Integral
本文从谐振子池中点粒子的前后向路径积分出发，导出了有惯性和无惯性的Fokker-Planck方程和Langevin方程。特别强调的是放在正确的运营商在时间演化运营商的顺序。关键的一步是评估的雅可比矩阵与延迟时间导数的解析正则化。
Quantum decoherence reduction by increasing the thermal bath temperature
对于耦合到线性热浴的量子系统，众所周知的退相干速率随温度的增加不再适用于不同的浴动力学。这是通过一个简单的经典非线性浴，以及量子自旋玻色子模型。反常效应是由于浴光谱轮廓的温度依赖性。通过温度升高降低退相干可以与量子计算机的设计相关。
The quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases is sdudied, in which the two subsystems, a two-level system and a single-mode bosonic field, are in contact with either two individual heat baths or a common heat bath. It is found that in the individual heat-bath case, the JC model can only be thermalized when either the two heat baths have the same temperature or the coupling of the JC system to one of the two baths is turned off. In the common heat-bath case, the JC system can be thermalized irrespective of the bath tempera…
Comments on Extraction of Work from a Single Thermal Bath in the Quantum Regime
在PRL [1]中，作者声称表明“克劳修斯不等式可以被违反，甚至可以通过参数的循环变化从热浴中提取功（“永久移动”），并且这种行为的物理原因可以追溯到非平衡浴中的量子相干性（原文如此）"。
We study the dynamics of an open quantum system interacting with a non-thermal bath. Here, "non-thermal" means that the bath modes do not need to have the same temperature, but they have an effective temperature distribution. We find that, when a quantum system is interacting with such a non-thermal bath far from thermal equilibrium, it is no longer proper to use any coarse-grained Markovian description for the system, even when their coupling strength is quite weak. Especially, when there is coherent transition with strong interference strength in the quantum system, the Markovian master equa…
Decoherence by a spin thermal bath: Role of the spin-spin interactions and initial state of the bath
我们研究了两个耦合自旋与自旋浴环境相互作用的退相干。结果表明，环境中自旋之间的连通性和耦合强度对中心系统的退相干是至关重要的。对于各向异性的旋转浴，改变连接性或耦合强度会使中心系统的退相干从高斯衰减规律变为指数衰减规律。初始状态的环境中示出影响退相干过程中的一个定性的显着方式。
Analytic solution to the nonlinear generation of squeezed states in a thermal bath
本文使用Lindblad主方程研究热浴中损耗光学腔的压缩态非线性产生，推导出正交不确定度演化的精确闭式解，并详细揭示了热环境对正交压缩与二阶相干函数的降低作用。
Ground state cooling is not possible given initial system-thermal bath factorization
在本文中，我们证明了一个基本的约束冷却动力学意味着它是不可能的冷却，通过一个单一的系统浴量子演化，一个系统，嵌入在一个热环境下，其基态，如果初始状态是一个因式分解的产品的系统和浴状态。后者是一个关键的，但人为的假设往往包括在许多描述系统浴动态。类似的结论适用于“冷却”到系统的任何纯态。
We derive the work cost of using generalized thermal baths from the physical equivalence of quantum mechanics under unitary transformations. We demonstrate our method by considering a qubit extracting work from a single bath to amplify a cavity field. There, we find that only half of the work investment is converted into useful output, the rest being wasted as heat. These findings establish the method as a promising tool for studying quantum resources within the framework of classical thermodynamics.
Quantum heat transfer is analyzed in nonequilibrium two-qubits systems by applying the nonequilibrium polaron-transformed Redfield equation combined with full counting statistics. Steady state heat currents with weak and strong qubit-bath couplings are clearly unified. Within the two-terminal setup, the negative differential thermal conductance is unraveled with strong qubit-bath coupling and finite qubit splitting energy. The partially strong spin-boson interaction is sufficient to show the negative differential thermal conductance. Based on the three-terminal setup, that two-qubits are asymm…
Diverse models of engines energised by quantum-coherent, hence non-thermal, baths allow the engine efficiency to transgress the standard thermodynamic Carnot bound. These transgressions call for an elucidation of the underlying mechanisms. Here we show that non-thermal baths may impart not only heat, but also mechanical work to a machine. The Carnot bound is inapplicable to such a hybrid machine. Intriguingly, it may exhibit dual action, concurrently as engine and refrigerator, with up to 100% efficiency. We conclude that even though a machine powered by a quantum bath may exhibit an unconvent…
We study the entropy dynamics of a dephasing model, where a two-level system (TLS) is coupled with a squeezed thermal bath via non-demolition interaction. This model is exactly solvable, and the time dependent states of both the TLS and its bath can be obtained exactly. Based on these states, we calculate the entropy dynamics of both the TLS and the bath, and find that the dephasing rate of the system relies on the squeezing phase of the bath. In zero temperature and high temperature limits, we prove that both the system and bath entropy increases monotonically. Moreover, we find that the deph…
In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a two-level system entirely with a thermal bath. Based on a time-local master equation, it is found that the residue coherence survives even under a high-temperature bath as long as the long-time Lamb shift is exactly negative to the system transition frequency. This condition is generally met in the strong and even ultrastrong coupling regime that could be relaxed …
Decoherence by a spin thermal bath: Role of the spin-spin interactions
我们研究了两个耦合自旋与自旋浴环境相互作用的退相干。结果表明，环境中自旋之间的连通性和耦合强度对中心系统的退相干是至关重要的。改变连通性或耦合强度，中心系统的退相干从高斯衰减规律变为指数衰减规律。
One long-standing difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derivie a set of non-Markovian qua…
Qualitative model of a positive hydrogen peroxide ion in a thermal bath
本文提出热浴中氧氢原子对的定性模型，模拟显示稳定分子离子及分离原子均能稳定形成。
In this article we argue that thermal reservoirs (baths) are potentially useful resources in processes involving atoms interacting with quantized electromagnetic fields and their applications to quantum technologies. One may try to suppress the bath effects by means of dynamical control, but such control does not always yield the desired results. We wish instead to take advantage of bath effects, that do not obliterate "quantumness" in the system-bath compound. To this end, three possible approaches have been pursued by us: (i) Control of a quantum system faster than the correlation time of th…
Thermalization of finite complexity and its application to heat bath algorithmic cooling
本文提出基于碰撞模型的有限复杂度热操作，通过迭代协议实现亚浴温冷却，并通过引入量子比特机器提升冷却效率。
We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a moving heat bath and a static cold bath. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum system we obtain the total produced work, the efficiency and the efficiency at maxim…
We study quantum thermalization and thermal entanglement in the open quantum Rabi model (QRM), in which a two-level system and a single-mode bosonic field are coupled to either two individual heat baths or a common heat bath. By treating the QRM as an effective multilevel system and deriving global quantum master equations in the eigenstate representation of the QRM, we study the physical conditions for quantum thermalization of the open QRM. It is found that, in the individual heat-bath case, the QRM can only be thermalized when either the two heat baths have the same temperature or the QRM i…
We present a scheme for dissipatively generating maximal entanglement in a heralded manner. Our setup requires incoherent interactions with two thermal baths at different temperatures, but no source of work or control. A pair of $(d+1)$-dimensional quantum systems is first driven to an entangled steady state by the temperature gradient, and maximal entanglement in dimension $d$ can then be heralded via local filters. We discuss experimental prospects considering an implementation in superconducting systems.
Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
研究了自旋为1/2的粒子在局部外加磁场的影响下，与各向异性自旋环境在热平衡温度$T$下相互作用的时间演化.对于有限个自旋，本文给出了中心自旋约化密度矩阵的精确解析形式。无限数量的环境自旋的情况下，使用正常的高斯随机变量的重新标度浴运营商的收敛性进行了研究。在此限制下，我们推导出分析形式的反铁磁相互作用的布洛赫矢量的组件内浴，我们调查的短期和长期的行为减少动力学。讨论了外加磁场、各向异性和熔池温度对中心自旋退相干的影响。
We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science, 2003], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalisation temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalisation, therefore increasing the output power and the engine efficiency only when t…
Quantum Langevin equation from forward--backward path integral
从热振子池中量子系统的密度矩阵的Feynman-Veron前-后向路径积分表示导出量子朗之万方程。我们展示的机制，其中经典的，$c$值的噪声在Feynman-Vernon理论变成一个运营商值的量子噪声履行特征交换关系所需的时间演化的量子朗之万方程的么正性。
Berry phase in open quantum systems: a quantum Langevin equation approach
利用量子朗之万方法，研究了具有缓变哈密顿量的二能级系统在缓变磁场中的演化，该系统的模型为自旋为1/2，与量子环境相互作用的模型为谐振子池.这允许容易地获得耗散时间和修正的贝里阶段的情况下的绝热循环演变。
We studied a single atom trapped in an optical tweezer interacting with a thermal bath of ultracold atoms of a different species. Because of the collisions between the trapped atom and the bath atoms, the trapped atom undergoes changes in its vibrational states occupation to reach thermal equilibrium with the bath. By using Monte Carlo simulations, we characterized the single atom's thermalization process, and we studied how this can be used for cooling. Our simulations demonstrate that, within known experimental limitations, it is feasible to cool a trapped single atom with a thermal bath.
A class of autonomous quantum heat baths satisfying the eigenstate thermalization hypothesis (ETH) criteria is proposed. We show that such systems are expected to cause thermal relaxation of much smaller quantum systems coupled to one of the baths local observables. The process of thermalization is examined through residual fluctuations of local observables of the bath around their thermal values predicted by ETH. It is shown that such fluctuations perturb the small quantum system causing its decoherence to the thermal state. As an example, we investigate theoretically and numerically thermali…
Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
本综述基于独立振子模型，简要介绍振子的量子朗之万方程及其稳态热力学，涵盖能量均分定理的量子对应、自由能、熵、比热、第三定律、耗散抗磁性、动量耦合及涨落定理。
Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is purely algebraic, in terms of the coefficients of the equation. In a second part, we consider general quantum Langevin equations and we prove that they can always be split into a maximal part driven by classical noises and a purely quantum one.
Thermalisation by a boson bath in a pure state
我们考虑一个与谐振子热浴弱耦合的量子系统。众所周知，这种玻色子浴最初在热平衡时使系统热化。我们表明，假设先验的平衡态是没有必要获得系统的热化。我们确定了完整的薛定谔时间演化的子系统的兴趣的初始纯产品状态的复合系统所考虑的系统和浴。我们发现，该系统松弛到正则平衡，几乎所有的初始纯浴态的宏观定义的能量。系统渐近热态的温度由初始浴态的能量确定为相应的微正则温度。此外，该系统的时间演化与假设玻色子浴最初在该温度下处于热平衡时获得的时间演化相同。我们的方法的一个重要组成部分是适用于其他浴，我们确定的浴功能，这是必要的热化研究。
One-dimensional Dirac oscillator in a thermal bath
我们分析了热浴中的一维狄拉克振子。我们发现，在更高的温度下，热容是一维谐振子热容的两倍。
Quantum speed limits for an open system in contact with a thermal bath
该研究证明了耦合热浴的量子系统量子演化速度的严格基本界，该界基于系统-浴哈密顿量的少体可观测量期望值，不依赖马尔可夫近似，可适用于弱系统-浴耦合极限之外的场景。
Thermal-bath effects in quantum quenches within quantum critical regimes
本文研究量子临界多体系统在含热浴的两类量子猝灭协议下的非平衡动力学，提出含温度与衰减率标度变量的扩展标度理论，并以Kitaev线/量子Ising链结合Lindblad热浴模型加以验证。
Entanglement Dynamics in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Dissipative interaction
该论文已被0901.0404取代，因此已撤回
Non-equilibrium states of quantum systems in contact with thermal baths help telling environments with different temperatures or different statistics apart. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that non-equilibrium states are not universally optimal, and detail the conditions in which it becomes convenient to wai…
We make a detailed comparison between entanglement harvesting for uniformly accelerated detectors in vacuum and static ones in a thermal bath at the Unruh temperature and find that, for a small energy gap relative to the Heisenberg energy of the detectors, static detectors in the thermal bath can harvest more entanglement and possess a comparatively larger harvesting-achievable range than the uniformly accelerated ones; however, as the energy gap grows sufficiently large, the uniformly accelerated detectors are instead likely to harvest more entanglement and possess a relatively larger harvest…
We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalizat…
A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail. This allows to distinguish a markovian semi-classical approach, due to Bedeaux and Mazur, from a non-markovian full quantum approach, due to to Ford, Kac and Mazur. The quantum-fluctuation-dissipation theorem is seen to be incompatible with a markov…
We present an alternative method for describing the evolution of a mode of the quantized electromagnetic field in contact with a finite temperature thermal bath. We use the expansion of the field density operator in terms of coherent states and the related Glauber-Sudarshan $P$-function in phase space. The method allows us to obtain analytical expressions of the system's time-evolved $P$-function without needing to solve the corresponding master equation.
We study the performance of quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we discover that reshaping of the window of performance is a central outcome of strong system-bath couplings. This alteration of the cooling window stems from the dominant role of parameter renormalization at strong couplings. We further show that strong coupling admit…
Influence of thermal bath on Pancharatnam-Berry phase in an accelerated frame
本文研究匀加速原子的 Pancharatnam-Berry 相位，发现场的热性质及 Unruh 热浴与真实热浴的交换对称性会影响相位，但实验所需高温超出当前技术能力。
Dense dipole-dipole-coupled two-level systems in a thermal bath
本文研究热浴中稠密二能级发射体系综的量子动力学，证明在弱热浴和较强偶极-偶极耦合条件下自发散射光场具有量子性质，并揭示集体光子强度受热浴强度调制。
Coherent oscillation in a linear quantum system coupled to a thermal bath
我们考虑的时间发展的密度矩阵的系统耦合到一个热浴，在模型中，超越了标准的两级系统，通过添加的能量激发自由度，并通过一个更复杂的代数取代自旋代数的可能性。我们发现的条件下，增加耦合到浴以上的一定水平降低了熵产生的速率，其中的限制行为是一个无耗散的正弦振荡，可以解释为许多模式的非耦合系统的同步。
The thermodynamic properties of Davydov-Scott's protein model in thermal bath
采用Lindblad开放量子系统方法研究了Davydov-Scott单体与热浴接触的热力学性质。用路径积分方法研究了林德布拉德方程。结果表明，环境效应对比热的影响是破坏性的，酰胺-I和酰胺位之间的相互作用对稳定的Davydov-Scott单体是不利的。
Temperature determines the relative probability of observing a physical system in an energy state when that system is energetically in equilibrium with its environment. In this paper, we present a theory for engineering the temperature of a quantum system different from its ambient temperature. We define criteria for an engineered quantum bath that, when coupled to a quantum system with Hamiltonian $H$, drives the system to the equilibrium state $\frac{e^{-H/T}}{\rm{Tr}(e^{-H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital quantum metropolis algorithm…
In this article we explore the set of thermal operations from a mathematical and topological point of view. First we introduce the concept of Hamiltonians with resonant spectrum with respect to some reference Hamiltonian, followed by proving that when defining thermal operations it suffices to only consider bath Hamiltonians which satisfy this resonance property. Next we investigate continuity of the set of thermal operations in certain parameters, such as energies of the system and temperature of the bath. We will see that the set of thermal operations changes discontinuously with respect to …
Open quantum systems with particle and bath driven by time-dependent fields
本文推导了粒子与浴均受外部含时场驱动的开放量子系统的广义量子朗之万方程及修正的涨落-耗散关系，并给出交流条件下量子奈奎斯特噪声的新形式，适用于5G/6G及量子技术。
We show that certain coherences, termed as heat-exchange coherences, which contribute to the thermalization process of a quantum probe in a repeated interactions scheme, can modify the spectral response of the probe system. We suggest to use the power spectrum as a way to experimentally assess the apparent temperature of non-thermal atomic clusters carrying such coherences and also prove that it is useful to measure the corresponding thermalization time of the probe, assuming some information is provided on the nature of the bath. We explore this idea in two examples in which the probe is assu…
Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath, are studied. The reduced density matrix is solved using the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied, calculating off-diagonal elements of the density matrix, spatiotemporal dispersion, purity and quantum mutual information. We find a characteristic time-scale pointing out when this coherence is maximum. In addition, a Wigner-like distribution in the phase-space (lat…
The Schrödinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the…
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