Quantum-mechanical nonperturbative response of driven chaotic mesoscopic systems

Consider a time-dependent Hamiltonian H(Q,P;x(t)) with periodic driving x(t) = Asin(Omegat). It is assumed that the classical dynamics is chaotic, and that its power spectrum extends over some frequency range |omega|A(prt), where A(prt) approximately Planck's over 2pi, the system may have a relatively strong response for Omega>omega(cl) due to QM nonperturbative effect.     

Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian, which evolves the quantum state with a dissipative dynamics. We also show that if the integration over the noisy field is done for the time evolution of the density matrix, a gain contribution from the fluctuations can be accessed in addition to the loss one from the non-hermitian Hamiltonian dynamics. We illustrate our study by computing analytically the effective non-Hermitian Hamiltonian, which we found to be the complex frequency harmonic oscillator, with a known evolution operator. It leads to space and time localisation, a common feature of noisy quantum systems in general applications.     

Quantum suppression of microwave ionization of Rydberg atoms at high scaled frequency

Microwave ionization of Rydberg atoms is well described as the onset of classical chaos when the microwave frequency omega is less than the Kepler frequency 1/n(3). However, when omega>1/n(3), i.e., at high scaled frequency Omega=omegan(3)>1, classical ionization is predicted to be suppressed by quantum interference, an analogue to Anderson localization in a solid. Using 17.55 GHz microwave fields we have observed the ionization of Sr Rydberg atoms in the regime 1相似文献   

Gauge covariant construction of the coherent states for a time-dependent harmonic oscillator by algebraic dynamical method

Time-dependent coherent states for a time-dependent harmonic oscillator are constructed in the framework of algebraic dynamics. These coherent states are gauge-covariant, and its time evolution is governed only by the solutions of a linear differential equation which describes the motion of the corresponding classical timedependent harmonic oscillator. Its non-classical and quantum statistical properties can thus be controlled by a proper choice of the frequency of the harmonic oscillator. Our coherent states reduce to Glauber coherent states in the case as the frequency is independent of time.     

Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

It is shown that the effective Hamiltonian representation, as it is formulated in author??s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are ??locked?? inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.     

Two-state system coupled to a boson mode: Quantum dynamics and classical approximations

The relation between classical and quantum mechanical integrability is investigated for a boson mode coupled to a two-level system. Different semi-classical approximations of this system are considered which are obtained by (i) factorization of expectation values of the two-state variable and the boson, (ii) making a WKB-type approximation, (iii) replacing the boson by a classical field of constant amplitude and fixed frequency and (iv) putting the boson into a self-consistent coherent state. The results vary considerably and include cases of non-integrable and integrable classical dynamics. Quantum mechanically the system is found to satisfy a criterion of quantum mechanical integrability, which we formulate, but the separated Hamiltonian of the boson alone does not have a well-defined classical limit. Numerical results for the energy spectrum and expectation values are obtained, which show a high degree of regularity but also display overlapping avoided crossings usually associated with non-integrable Hamiltonians. The exact dynamics of the occupation probabilities of the two levels is also analysed numerically. The dependence of quantum mechanical recurrence effects (in quantum optics known as revivals) on coupling strength, frequency detuning and initial conditions is studied. The revivals are found to disappear in the case of strong coupling. The Fourier spectra of the dynamical expectation values are also calculated     

Evaluation of an algebraic model for the vibrations of water,effects of a discrete symmetry

We evaluate the dynamics of an algebraic model Hamiltonian for the vibrational motion of the water molecule. We pay special attention to the effects of the discrete symmetry of order 2 of the model. For a comparison between the quantum dynamics and the classical dynamics it is necessary to desymmetrize such quantum states which are based on types of motion which come in symmetry related pairs. For the other states based on motion invariant under the symmetry operation a desymmetrization would be meaningless. The desymmetrized quantum states show a simple connection to the guiding motions of the classical dynamics which can be used for a complete assignment of the states even though the system is not integrable in the sense of Liouville and shows chaotic behaviour in large parts of the classical phase space.     

Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of K$K$s to combine with Lewis–Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in detail.     

Ultralocal scalar field models

In this paper the quantum theory of ultralocal scalar fields is developed. Such fields are distinguished by the independent temporal development of the field at each spacial point. Although the classical theories fit into the canonical framework, this is not the case for the quantum theories (with the exception of the free field). Explicit operator constructions are given for the field and the Hamiltonian as well as several other operators, and the calculation of the truncated vacuum expectation values is reduced to an associated single degree of freedom calculation. It is shown that construction of the Hamiltonian from the field, as well as the transition from the interaction to the noninteracting theories entails various infinite renormalizations which are made explicit.     

On the Interaction of Massive Photons and Mechanical Oscillators in Cavity Optomechanics: Basic Model and Quantization

This study investigates the theoretical aspects of the interaction between photons with mass and a mechanical oscillator as drawn within the framework of cavity optomechanics. The study employs Proca theory as the mathematical framework to initially describe the dynamics of massive photons in a Fabry-Perot cavity with a movable mass, both in classical and quantum scenarios. It quantifies the modifications induced by the nonzero photon mass, considering first- and second-order effects, and derives expressions for the amplification of radiation pressure resulting from the presence of nonzero photon mass. Additionally, it derives the Hamiltonian of the quantum optomechanical system, incorporating the effects of photon mass at first and second order. It anticipates that experimental realization of massive optomechanics can be achieved by utilizing Proca material, which is a spatio-temporally dispersive material that exhibits behavior equivalent to Proca theory in a vacuum, thus enabling the study of the interaction between massive photons and mechanical systems in cavity-based optomechanical setups (referred to as massive cavity optomechanics). The study presented here caters to a diverse audience with an interest in the analysis and measurement of interactions among massive objects at the quantum scale.     

Extending Newton's law from nonlocal-in-time kinetic energy

We study a new equation of motion derived from a context of classical Newtonian mechanics by replacing the kinetic energy with a form of nonlocal-in-time kinetic energy. It leads to a hypothetical extension of Newton's second law of motion. In a first stage the obtainable solution form is studied by considering an unknown value for the nonlocality time extent. This is done in relation to higher-order Euler-Lagrange equations and a Hamiltonian framework. In a second stage the free particle case and harmonic oscillator case are studied and compared with quantum mechanical results. For a free particle it is shown that the solution form is a superposition of the classical straight line motion and a Fourier series. We discuss the link with quanta interpretations made in Pais-Uhlenbeck oscillators. The discrete nature emerges from the continuous time setting through application of the least action principle. The harmonic oscillator case leads to energy levels that approximately correspond to the quantum harmonic oscillator levels. The solution to the extended Newton equation also admits a quantization of the nonlocality time extent, which is determined by the classical oscillator frequency. The extended equation suggests a new possible way for understanding the relationship between classical and quantum mechanics.     

Correlation Dynamics of Three-Qubit System Under a Classical Dephasing Environment

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their frequency fluctuations as caused by dephasing noisy environments described by Ornstein-Uhlenbeck (OU) processes, we study the dynamics of quantum correlations, including entanglement and quantum discord. Of course, in this article, we use two definitions for the quantum discord (global quantum discord and quantum dissension). We prepared initially our open system with the Greenberger-Horne-Zeilinger (GHZ) and W states and present the exact solutions for evolution dynamics of entanglement and quantum discord between three spins under both Markovian and non-Markovian regime of this classical noise. By comparison the dynamics of entanglement with that of quantum discord we find that entanglement can be more robust than quantum discord against this noise. It is shown that by considering non-Markovian extensions the survival time of correlations prolong. Also, we compare the results of two definitions of the quantum discord and show that the quantum dissension is equal to the global quantum discord for GHZ state, but they are unequal for the W state.     

Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula

Letters in Mathematical Physics - We use the theory of Berezin–Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows...     

Applications of Noether conservation theorem to Hamiltonian systems

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.     

Quantum phase transitions in the sub-Ohmic spin-boson model: failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive mapping fails for the sub-Ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional, variantomega(s). Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.     

与双模光场作用的Λ型三能级原子及其二能级近似

从多能级原子与多模光场的相互作用哈密顿量出发,导出了Λ型三能级原子与双模光场的相互作用哈密顿量。在大失谐条件下将其化成等效的二能级形式-双模喇曼耦合模型。提出了该模型的一个改进型等效哈密顿量。该哈密顿量由两部分构成:一部为通常所谓的等效哈密顿量,另一部分描述原子能级的动态斯塔克移动。研究表明,在双模喇曼耦合模型的研究中,只考虑前者是不够的,还必须考虑后者。最后,我们研究了该系统中原子的动力学行为,发现崩塌-复苏的数目、崩塌时间和复苏时间均呈现新的特性。     

Critical frequency in nuclear chiral rotation

Self-consistent solutions for the so-called planar and chiral rotational bands in 132La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as Planck's omega(crit) approximately 0.5-0.6 MeV. However, the exact values of Planck's omega(crit) may vary, to an extent, depending on the microscopic model used, in particular, through the pairing correlations and/or calculated equilibrium deformations. The existence of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.     

与双模光场作用的Λ型三能级原子及其二能级近似

从多能级原子与多模光场的相互作用哈密顿量出发,导出了Λ型三能级原子与双模光场的相互作用哈密顿量．在大失谐条件下将其化成等效的二能级形式－双模喇曼耦合模型．提出了该模型的一个改进型等效哈密顿量．该哈密顿量由两部分构成：一部为通常所谓的等效哈密顿量,另一部分描述原子能级的动态斯塔克移动．研究表明,在双模喇曼耦合模型的研究中,只考虑前者是不够的,还必须考虑后者．最后,我们研究了该系统中原子的动力学行为,发现崩塌－复苏的数目、崩塌时间和复苏时间均呈现新的特性．     

Correlation dynamics of qubit-qutrit systems in a classical dephasing environment

We study the time evolution of classical and quantum correlations for hybrid qubit-qutrit systems in independent and common dephasing environments. Our discussion involves a comparative analysis of the Markovian dynamics of negativity, quantum discord, geometric measure of quantum discord and classical correlation. For the case of independent environments, we have demonstrated the phenomenon of sudden transition between classical and quantum decoherence for qubit-qutrit states. In the common environment case, we have shown that dynamics of quantum and geometric discords might be completely independent of each other for a certain time interval, although they tend to be eventually in accord.