John Gough
This paper has been withdrawn by the author. The central result is now included in quant-ph/0309056 (as in the journal publication!). An erratum on the Heisenberg perturbation series estimate is also included therein.
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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…
The non-Markovian dynamics of a charged particle linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field. The analytical expressions for the time-dependent and asymptotic friction and diffusion coefficients, cyclotron frequencies, variances of the coordinate and momentum, and orbital magnetic moments are derived. The role of magnetic field in the dissipation and diffusion processes is illustrated by several examples in the low- and high-temperature regimes. The localization phenomenon for a charged particle is observed. The orbital diamagnetism of …
This paper presents a non-Markovian coherent feedback scheme to control single quantum dot systems. The feedback loop is closed via a quantum tunneling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyze the Green's function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. This effecti…
Langevin Theory of Non-Markovian Quantum Dynamics: Application to Delayed Coherent Feedback and the Laser Linewidth
本文提出了适用于非马尔可夫量子动力学的通用朗之万框架，将其应用于延迟相干反馈问题，重现并预测了激光线宽的窄化效应，且框架可扩展至多体系统。
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving such integro-differential equations. Physically motivated example calculations are performed to demonstrate the accuracy and convergence of the method.
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…
Numerical Framework for Multimode Jaynes- and Tavis-Cummings Models Incorporating the Modified Langevin Noise Formalism: Non-Markovian Analysis of Atom-Field Interactions in Dissipative Electromagnetic Environments
本文提出一种结合修正Langevin噪声形式与多模Jaynes-和Tavis-Cummings模型的数值框架，通过有限元方法求解边界和介质辅助场模式，实现了对耗散电磁环境中原子-场相互作用的非马尔可夫分析，并经四个算例验证了其作为真值模拟器的准确性。
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications t…
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.
Examination of classical simulations for Heisenberg-Langevin equations for spin-1/2
本文研究了通过经典广义Langevin方程模拟自旋动力学的方法，通过修改哈密顿量与Weisskopf-Wigner理论进行比较，探讨其在零温与高温极限下的表现。
Semiclassical path integral expression for a quantum system coupled to a harmonic bath is derived based on the stationary phase condition. It is discovered that the system path is non-Markovian. Most strikingly, the system path not only couples to its past (as in the Langevin equation), but also to its future, i.e. the equation of motion for the system is an integro-differential equation that involves all times. Numerical tests are performed to confirm that the future-involved term is indeed necessary. Because of the future-non-Markovian nature of the equation, the numerical solution cannot be…
The dynamical behavior of quantum coherence of a displaced squeezed thermal state in contact with an external bath is discussed in the present work. We use a Fano-Anderson type of Hamiltonian to model the environment and solve the quantum Langevin equation. From the solution of the quantum Langevin equation we obtain the Green's functions which are used to calculate the expectation value of the quadrature operators which are in turn used to construct the covariance matrix. We use a relative entropy based measure to calculate the quantum coherence of the mode. The single mode squeezed thermal s…
Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises
本研究采用泛函微扰方法推导含非马尔可夫反作用噪声的非线性朗之万方程，可处理任意镜面位移，为高精度量子光力学实验提供理论支持。
A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the classical Levy-Khinchin formula are elucidated. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equations. Important topics for future investigation are outlined.
We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the system using two approaches: Quantum Mechanics and Bohmian Theory. Our results show that the predictions of the two theories are inherently different in real conditions. Nevertheless, the Langevin equation obtained by Bohmian approach could be reduced to the quantum one, when the vibrational frequency of the central system is high enough compared to the maxim…
We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal noise contribution, using the quantum Langevin approach. We show that the standard quantum Langevin equations, supplemented with the appropriate non-Markovian correlation functions, provide an adequate description of Brownian motion.
The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain the Greens functions which are used to compute the time evolved first and second moments of the quadrature operators. From the quadrature operator moments, we construct the covariance matrix which is used to measure the coherence in the system. The coherence is measured using the relative entropy of coherence measure. We consider three different classes of spe…
In the previous paper, it has been proved that elastic scattering processes of two quantum particles are always accompanied with nonlocal processes. Furthermore, it is found that setting an additional Hamiltonian after the originally scattering one can help to describe the two type of processes in a united frame. Here we discuss the contribution of this additional Hamiltonian to irreversible process in isolated quantum systems. The use of the Hamiltonian can induce the non-Markovian Langevin equation, showing a complex memory effect, and thus revealing the irreversible essence of isolated syst…
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…
In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non- Markovian. A dire…
The piezoelectric optomechanical devices supply a promising experimental platform to realize the coherent and effective control and measurement of optical circuits working in Terahertz (THz) frequencies via superconducting electron devices typically working in Radio (MHz) frequencies. However, quantum fluctuations are unavoidable when the size of mechanical oscillators enters into the nanoscale. The consequences of the noisy environment are still challenging due to the lack of analytical tools. In this paper, a semi-classical and full-quantum model of piezoelectric optomechanical systems coupl…
The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr{ö}dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born--Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state …
We establish a quantum functional central limit for the dynamics of a system coupled to a Fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian limit, we realize the open dynamical evolution of the system as an adapted quantum stochastic process driven by Fermionic Noise.
We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This allows quantum Langevin equations to be calculated, which have a classical form except for additional quantum noise terms. In practical calculations, it is more useful to transform to Wigner or +$P$ quasi-pro…
The application of quantum Langevin equations for the study of non-equilibrium relaxations is illustrated in the exactly solved quantum spherical model. Tutorial sections on the physical background of non-markovian quantum noise, the spherical model quantum phase transition, the long-time limit of the quantum Langevin equation of the spherical model and physical ageing are followed by a brief review of the solution of the non-markovian time-dependent spherical constraint and about the consequences for quantum ageing at zero temperature, after a quantum quench.
We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from below by a modified Wasserstein distance between the initial and final states, thus strengthening the Clausius inequality in the reversible-Markov case. The modified metric can be regarded as a discrete-state generalization of the Wasserstein metric, which has been used to bound dissipation in continuous-state Langevin systems. Notably, the derived bounds ca…
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations…
An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment metho…
Non-Markovian amplitude damping in a central spin model with random couplings
本文研究随机耦合中心自旋模型中的非马尔可夫动力学，发现动力学特性取决于环境记忆与系统-环境相互作用结构，且QFI流在弱耦合和近共振区域可能失效而BLP度量仍能检测信息回流，揭示了记忆效应物理起源并指出随机性与调制可用于设计抗噪声量子技术。
We investigate a `pseudo thermalization' effect, where an open quantum system coupled to several non-Markovian reservoirs presents an emergent thermal behaviour in spite of its coupling to a non-equilibrated environment. The thermal behaviour is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a mic…
The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $n\to\infty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the un…
Limitations of the Markovian approximation in the harmonic oscillator
本文研究了两种典型单个阻尼谐振子模型中马尔可夫近似的局限性，揭示了其在经典极限、厄恩费斯特定理违反、正性破裂及热化行为异常等方面的问题，强调了非马尔可夫框架在开放量子动力学描述中的重要性。
Quantum-Plasmonic Dynamics Modeled via a Modified Langevin Noise Formalism: Numerical Studies of Single-Photon Emission and Two-Photon Interference
本文提出了一种改进的Langevin噪声形式，用于建模量子等离子体动力学，展示了在单光子发射和双光子干涉中的应用及非马尔可夫动力学的分析。
Role of System-Bath Interaction in Non-Markovian Quantum Brownian Otto Cycles
通过解析求解海森堡-朗之万方程，研究非马尔可夫强耦合对量子奥托循环的影响，发现等容过程中相互作用能的变化对功和热有贡献，且会降低发动机的功输出。
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a Gaussian state. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stocha…
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