Gustavo Lopez, Xaman-Ek Lopez, Gabriel Gonzalez
For a one-dimensional dissipative system with position depending coefficient, two constant of motion are deduce. These constants of motion bring about two Hamiltonians to describe the dynamics of same classical system. However, their quantization describe the dynamics of two completely different quantum systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown that those ambiguities do not affect the fate of the classical singularity, demonstrating that the absence of a singularity in loop quantum cosmology is a robust implication of the general quantization scheme. The calculations also allow conclusions about modified operators in the full theory. In particular, using holonomies in a non-fundamental …
We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the Hamiltonian, we quantize canonically the classical particle in a viscous media. We study the free quantum particle in a viscous media and the dissipative quantum tunnelling. It is found that the dissipation influences tunnelling probability by a factor that closely resembles the result of Caldeira and Leggett.
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.
For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe the dynamics of the same classical system. However, their quantization and the associated statistical mechanics (for an ensemble of particles) describe two completely different quantum and statistical systems. This is shown at first order in the dissipative parameter.
A canonical quantization scheme is represented for a quantum system interacting with a nonlinear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The nonlinear response equation of the environment against the motion of the main system is obtained. The nonlinear Langevin-schrödinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of nonlinearity of the environment is investigated on the spontaneous emission of an initially excited two lev…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is shown a great difference on the quantization of both approaches and the ambiguities arisen by using the quantization on the constants of motion.
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative systems. Here, as a further application of this formalism, we consider a dissipative system of charged particles interacting with an external time dependent electric field. Such a system has been investigated by Buch and Denman, and two distinct solutions with completely different structure have been obtained for Schrödinger's equation in two different gauges. However, by generalizing the gauge transformations to the phase space and using the extende…
Noncritical strings in the "coupling constant" phase space and bosonic string in the affine-metric curved space are dissipative systems. But the quantum descriptions of the dissipative systems have well known ambiguities. We suggest some approach to solve the problems of this description. The generalized Poisson algebra for dissipative systems is considered.
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding Poisson tensor is allowed to explicitly depend on time. Starting from this pseudo-Hamiltonian formulation we develop a consistent deformation quantization procedure involving a non-stationary star-product $*_t$ and an ``extended'' operator of time derivative $D_t=\partial_t+...$, differentiating the $\ast_t$-product. As in the usual case, the $\ast_t$-algebra of p…
Dissipative Channels Determine Open Electromagnetic Quantization
提出一种开放电磁系统的量子化方案，通过麦克斯韦算子的耗散几何识别储层，将涨落通道分为介质辅助和边界辅助两类，并导出格林函数输入输出关系，应用于有损结构和光子集成电路。
Basing on the Chetaev's theorem on stable trajectories in dynamics in the presence of dissipative forces we obtain a generalized stability condition for Hamiltonian systems that has the form of the Schrodinger equation. We show that the energy of the dissipative forces generating generalized Chetaev's stability condition exactly coincides with Bohm's "quantum" potential. Using the principle of least action of perturbation we prove that the Bohmian quantum mechanics complemented with the Chetaev's generalized theorem does not have hidden variables.
A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific case of suggested quantization. This approach allows to define consistent quantization procedure for non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction (generalized Lorenz-Rossler-Leipnik-Newton equation), the Fokker-Planck-type system and Lorenz-type system are…
Nowadays, two of the most prospering fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation plays a crucial role. In the present work we formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned, and creates a theoretical frame to overcome these issues in the future. Based on the Lagrangian framework of the damped spring system, the canonically conjugated pairs and the Hamiltonian of the system are obtained, by which the quantization procedure can be started and consistently applied. As a result,…
Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
本文重新表述三次量子化技术，统一连接Lindblad主方程、Wigner函数和Keldysh作用量三种开放量子系统方法，揭示二次Lindblad算符中的基本耗散对称性，并将其应用于耗散非线性振子获得新的精确结果。
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The 't Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quant…
Extending third quantization with commuting observables: a dissipative spin-boson model
本研究针对含玻色子与自旋的开放量子系统的Lindblad-Gorini-Kossakowski-Sudarshan主方程，利用可交换自旋算符耦合的特性扩展第三次量子化方法，求解其谱问题与初值问题，并以单个开放自旋-玻色子模型为例进行了详细推导。
The quantization of plasmons has been analyzed mostly under the assumption of an infinite-sized bulk medium interacting with the electromagnetic field. We reformulate it for finite-size media, such as metallic or dielectric nano-structures, highlighting sharp differences. By diagonalizing the Hamiltonian by means of a Lippmann-Schwinger equation, we show the contribution of two sets of bosonic operators, one stemming from medium fluctuations, and one from the electromagnetic field. The results apply to general models including dissipative and dispersive responses.
We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multi-plasmon/photon Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission.…
A Nonrecursive Lindblad Quantization of Dissipative Polynomial Dynamics
本文提出一种非递归的 Lindblad 量子化方法，将任意平面多项式耗散流直接映射为开放量子系统，无需递归消除低阶项，并在半经典极限下恢复经典动力学特征，可用于设计具有指定经典结构的量子系统。
Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the physically relevant information that the motion is continuous and non-dissipative. Here we focus on the quantum theory of scalar fields. We provide an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schroedinger representation.
Within the framework of a phenomenological quantization scheme, we present the quantization of the electromagnetic field in the presence of a moving absorptive and dispersive magneto-dielectric slab (MDS) with uniform velocity in the direction parallel to its interface. We derive the quantum input-output relations for the case that quantum states propagate perpendicularly to the moving MDS.We thoroughly investigate the impact of the motion of the movingMDS on quantum properties of the incident states. To illustrate this, by modeling the dispersive and dissipative effects of the slab by the Lor…
Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schrodinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm "quantum" potential. Within the framework of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave func…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of dynamical invariants previously proposed by the authors, in which fundamental importance is given to the linear invariants of the oscillator.
Kadanoff-Baym equations for interacting systems with dissipative Lindbladian dynamics
本文提出一种针对耗散NEGF理论的二次量子化方法，通过重新表述Keldysh思想以适应Lindbladian动力学并扩展Kadanoff-Baym方程，实现了关联和耗散的实时模拟，用于探索材料的瞬态和稳态电子、输运及光学性质变化。
Quantum Quasinormal Mode Theory for Dissipative Nano-Optics and Magnetodielectric Cavity Quantum Electrodynamics
本文提出了一种基于宏观QED和复坐标变换的统一理论框架，实现对磁电谐振腔的准正常模式量化，为量子纳米光学实验提供了理论基础。
We study the quantization of many-body systems in three dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear gauge conditions, and discuss their Gribov ambiguities and commutator algebra. We construct the momentum operators, inner-product and Hamiltonian in those gauges, for systems with and without translation invariance. The analogy with the quantization of non-Abelian Yang-Mills theories in non-covariant gauges is emphasized. Our results are applied to quasi-rigid systems in the Eckart frame.
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases we discuss their Gribov ambiguities and commutator algebra. We construct the momentum operators, inner-product and Hamiltonian in both types of gauges, for systems with and without translation invariance. The analogy with the quantization of QED in non-covariant gauges is emphasized. Our results are applied to quasi-rigid systems in the Eckart frame.
Quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) is analyzed using both path integral and canonical quantization schemes within the framework of Hilbert-Schmidt operator formulation. We adopt a method which is distinct from the one which employs 't Hooft's scheme of quantization, carried out earlier in the literature where the ambient space was taken to be commutative. Our quantization shows that we end up finally again with a Bateman system except that the damping factor undergoes renormalization. The corresponding expression shows tha…
Various aspects of dissipative and nondissipative decoherence of Rabi oscillations are discussed in the context of field quantization in alternative representations of CCR. Theory is confronted with experiment, and a possibility of more conclusive tests is analyzed.
One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Lienard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence do…
We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that governs the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean qu…
Calculating strongly correlated ground states from the non-Markovian dissipative dynamics of Gaussian fermions
该研究介绍相互作用费米子哈密顿量基态与纯耗散开放量子系统非平衡稳态的映射，通过第三次量子化将费米 - 哈伯德哈密顿量映射到作用于马约拉纳费米子的林德布拉德跃迁算符，虽单个轨迹可高效模拟，但总体计算成本仍高，需进一步研究非马尔可夫解开效率。
Quantization and Mirror Reduction Do Not Commute in Hamiltonian Embeddings of Nonreciprocal Dynamics
该研究证明非互易动力学的哈密顿嵌入在经典层面精确，但其正则量子化与镜像约化不对易，导致半经典奇异构造，并给出对数对应时间公式。
An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency $ω_q$, the environment only has to be modeled close to this frequency. Different from alternative approaches, we show that this goal can be achieved by modeling the environment with only few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We de…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce unequivalent dynamical behaviors. The relation with a formal treatment of the constraint is discussed. While classically it is always possible to strictly enforce the constraint by setting to zero the energy stored in the motion normal to the constraint surface, the quantum description is far more sensitive to the reduction mechanism. Not only quantum dynamics…
Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
本研究通过Lindblad动力学和有效非厄米哈密顿量两种模型，探究三类耗散通道对二能级拓扑频率转换器量子化功率传输的影响，发现耗散会引发量子看门狗效应破坏功率传输，退相导致传输指数衰减，并揭示非厄米描述中存在非绝热过程。
A note on a classical dynamical system and its quantization
本文研究修改版Bateman系统，发现其量子化后不必然耗散，Hamiltonian随参数关系可表现为标准谐振子或包含倒置振子，并用阶梯算符分析了两种情况。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。