Deconfinement and phase diagram of bosons in a linear optical lattice with a particle reservoir

We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose-condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state.     

Controlling bistability by linear augmentation

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.     

A Lorentz-covariant interacting electron–photon system in one space dimension

Letters in Mathematical Physics - A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one...     

Effects of fields and anchoring on biaxial nematic ordering

Symmetry of a nematic liquid crystal phase is broken by an anchoring wall and also by an external field. Nematic system sandwiched between biaxial anchoring walls is introduced as a correspondent to a bulk nematic system exposed to a couple of fields, an electric field and a magnetic one in directions perpendicular to each other, and thermal behaviours of the system are studied. The crossover between a homeotropic structure and homogeneous one occurs, similarly to the bulk system in the fields, in which the anchoring condition of coexistence is shown to have the same expression as the one at the bulk. As to a characteristic phenomenon at the sandwiched system, it is proved that an appearance of a biaxial nematic order suppresses a uniaxial nematic order. A surface transition, i.e., a wetting phenomenon is shown to occur also in the biaxial nematics, even though the uniaxial order is suppressed therein.     

Study of “forbidden” atomic transitions on D2 line using Rb nano-cell placed in external magnetic field

In this paper the treatment of a three-level atom which is confined in a Fabry-Perot optical cavity with a nonlinear mirror is investigated. Despite the nonlinear effects we show that this system operates in two different regimes. In one regime the system shows conventional laser properties which is approximated by a semiclassical laser theory and in the other one the system displays new quantum properties which is approximated by an effective two-level atom. For validity of the behavior of the system in two different regimes computer simulations are implemented.     

Multiswitching compound antisynchronization of four chaotic systems

Based on three drive–one response system, in this article, the authors investigate a novel synchronization scheme for a class of chaotic systems. The new scheme, multiswitching compound antisynchronization (MSCoAS), is a notable extension of the earlier multiswitching schemes concerning only one drive–one response system model. The concept of multiswitching synchronization is extended to compound synchronization scheme such that the state variables of three drive systems antisynchronize with different state variables of the response system, simultaneously. The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, sufficient condition is obtained to achieve MSCoAS between four chaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed using Lorenz system in MATLAB to demonstrate the validity of the presented method.     

一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法

提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用. 关键词： 逆问题 耗散系统 Lagrange函数 Hamilton函数     

构造准正则变换的方法

给出构造Hamilton系统的准正则变换的方法,首先将Hamilton系统变换成Birkhoff系统,然后将Birkhoff系统作规范变换并实现Hamilton化. 指出对一个Hamilton系统存在多种准正则变换. 举例说明所得结果的应用. 关键词： Hamilton系统 准正则变换 Birkhoff系统 规范变换     

一种具有恒Lyapunov指数谱的混沌系统及其电路仿真

提出了一种新的具有恒Lyapunov指数谱的三维混沌系统,该系统含有六个参数,其中一个方程含有一个非线性乘积项,一个方程含有平方项.通过理论推导、数值仿真、Lyapunov维数、Poincare截面图、Lyapunov指数谱和分岔图研究了系统的动力学特性,并分析了不同参数变化对系统动力学行为的影响,其中,平方项系统参数变化时,系统的Lyapunov指数谱保持恒定,输出信号中的两维信号的幅值与参数呈幂函数关系变化,其指数为－1/2,第三维信号的幅值保持在同样的数值区间.最后,设计了该混沌系统的硬件电路并运用Multisim软件对该电路进行仿真实验,证实了该混沌系统的可实现性. 关键词： 混沌系统 恒Lyapunov指数谱 Poincare截面图 混沌电路     

Phase transitions in double-layered josephson junction arrays

A system of two parallel Josephson junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e. the vortices in one layer and the charges in the other. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses the temperature of vortex-unbinding transition. It further replaces the charge-unbinding transition by a crossover, which is smeared already for weak interlayer coupling.     

Thermodynamics under Dynamic Forcing

Beginning with a system that is governed by an arbitrary time-dependent Hamiltonian, we exhibit an existence proof for a unitary generator that has an arbitrary initial value and yet contact transforms the representation to one governed by any given kinematically equivalent Hamiltonian. By choosing the initial value of the unitary operator to be unity, we are able to compare the behaviour of the same system under two different Hamiltonians and the same initial state vector. We thus are able to establish that the eventual physical states evolving from two distinct initial quantum state vectors will become practically indistinguishable under one of the two Hamiltonians if and only if they do so under the other. For the restricted class of systems for which one of the two Hamiltonians is a time-independent energy operator, and also generates equilibrium thermodynamics, then the condition for merging under the time-dependent Hamiltonian is the same as under the time-independent one. The two states must have the same initial energy. As a special case of the above, we choose the time-independent Hamiltonian to be the relativistic energy measuring operator for the time-dependent Hamiltonian, as associated with the chosen initial time. If the system under the time-dependent Hamiltonian is such that its relativistic energy measuring operator for any fixed time generates equilibrium thermodynamics, then we are led rigorously to the conclusion that the instantaneous relativistic energy for the system under the time-dependent Hamiltonian is simply a well-defined function of time and depends only on the initial energy and not on any other initial conditions. For a composite system that is of the above type, and in addition consists of one very small system in contact with a very large one, which is called a generalized reservoir, we consider a specific initial physical state for the large system, and various states for the small one. The eventual dynamic state of the composite system is essentially independent of the initial state of the small system which has almost no influence on the total composite energy. Hence the eventual dynamic state of the small system is shown rigorously to be independent of its initial state. For a forced system with a time-dependent Hamiltonian, we discuss the assignment of equilibrium thermodynamic potentials to a representation with a time-independent Hamiltonian. We discuss the concept of a process under a time-dependent Hamiltonian. Such a process is a natural generalization of the static and quasi-static processes. Also, we verify all of the theory with both general and specific examples of electromagnetic interactions.     

Terahertz antiresonant-reflecting-hollow-waveguide-based directional coupler operating at antiresonant frequencies

We report a particular coupling phenomenon occurring in the directional coupler composed of two touching terahertz antiresonant reflecting hollow waveguides. Unlike conventional directional couplers where one even system mode and one odd system mode are excited, numerical results indicate that three (one even and two odd) system modes participate in the power transfer process at the antiresonant frequencies. As a result, the coupling length can be significantly reduced, and it is shown here to be less than 300 wavelengths.     

Bose-like few-fermion systems

It is shown that the specific heat of a few-fermion system with odd number fermions behaves differently from that of a few-fermion system with even number fermions. The specific heat of an even-number-fermion system behaves like a Bose one rather than a Fermi one.     

ATOMIC COHERENT POPULATION TRAPPING AND ITS APPLICATION IN A RAMAN-TYPE PHOTOIONIZATION SYSTEM WITH THREE BOUND STATES

We have studied the atomic coherent population trapping in a Raman-type, photoionization system with three bound states. The conditions for the system having two or one stable eigenstate are given. The influences of Fano asymmetric factors on the coberent population transfer are also analyzed.It is found that the property of the system having on]y one population trapping state consisting of the ground state, and one excited state, can be utilized to transfer the atomic initial population into one excited state.     

Chaotic dynamics of coupled two-level atoms in the optical cavity

Spin systems are one of the most promising candidates for quantum computation. At the same time, control of a system's quantum state during time evolution is one of the main problems. It is usually considered that in magnetic resonance the so-called resonance condition is sufficient to control the spin system. However, because of the nonlinearity of the system, obstructions to the control of the system's quantum state may emerge. In particular, the quantum dynamics of coupled two-level atoms in the optical cavity are studied in this work. The problem under consideration is a generalization of the paradigmatic model for Cavity Quantum Electrodynamics of the Jaynes-Cummings model in the case of interacting spins. In this work, it is shown that the dynamics are chaotic when taking into account the center-of-mass motion of the system and the recoil effect. Furthermore, even in the case of zero detuning, chaotic dynamics emerge in the system. It is also shown in this work that, because of the chaotic dynamics the system executes an irreversible transition from a pure quantum-mechanical state to a mixed one. Irreversibility, in turn, is an obstacle for controlling the state of the quantum-mechanical system.     

Path-dependent phase shifts in isolated systems

The Aharonov-Casher effect in a closed system is discussed. In this model, the charge on the wire is produced by a conducting bar moving in a magnetic field. If one considers the neutron to be a classical particle and the moving bar to be a quantum object, then the wave function of the bar acquires a phase shift equal in magnitude but opposite in sign to the usual phase shift of the neutron wave function. It is also shown that in any closed system, a path-dependent phase shift of one part of the system is always accompanied by an opposite phase shift of the remainder of the system. This result follows directly from the principle of least action.     

Local detection of entanglement

We construct an explicit model where it can be established if a two mode pure Gaussian system is entangled or not by acting only on one of the parts that constitute the system. Measuring the dispersion in momentum and the time evolution of the dispersion in position of one particle we can tell if entanglement is present as well as the degree of entanglement of the system.     

On the presence of spatial pattern formation in a bistable dynamical system

The aim is to investigate whether in a structural bistable reaction-diffusion system pattern formation may emerge simultaneously from both steady states. Therefore, a dynamical system is modelled by three coupled nonlinear differential equations from which synergetic ordering may arise. In addition, the nonlinear terms are chosen such that the homogeneous system is governed by the canonical form of a cusp bifurcation in a two-dimensional control space. Thus, structural bistability is established. Based on a linear stability analysis the region of bistability is decomposed into four different domains in the control plane. It is shown that in one of these domains self-organization can lead to pattern formation from both steady states simultaneously. In two other domains self-organization can arise from only one steady state and finally in one domain patterning is impossible. An expression for the wavelength of a spatial structure is derived and discussed in terms of parameters of the system. As a possible application of the present results a crystal under irradiation with particles of high energy is considered. It is demonstrated for the case of steel that the parameters of the system can be chosen such that a two-fold spatial instability for irradiation induced cavities may emerge.     

Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament

The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequence of constants of motion in involution. An algebraic framework is given with the aim of describing the differential geometry of this system and a geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but a similar one. As a related topic, a remark on the inspection of J. Langer and R. Perline (J. Nonlinear Sci. 1 (1991), 71) is given.     

Range of forces and broken symmetries in many-body systems

It is argued that for a many-body system with short range forces the commutators between local operators at different times will be fast decreasing for large spatial separations.This allows the adaptation of many discussions in relativistic field theories to the case of a many-body system with short range forces. In particular one has the result that a spontaneous breakdown in symmetry implies the existence of excitations of arbitrarily small energy. However this result has essentially only one application: We know that the Galilei invariance is always broken (in a medium of finite density). Therefore one concludes that in a many-body system with short range forces there can never be an energy gap.Supported by the National Science Foundation.