Dynamics of two-level systems beyond the rotating-wave approximation

We study the dynamics of quantum discord and entanglement in a two-qubit system coupled to the same quantized field without rotating-wave approximation. In the absence of initial correlations, we show that maximal quantum discord (entanglement) can be obtained in the strong coupling regime. Analytical result corresponding to an effective Hamiltonian is given. In a deep strong coupling regime, sudden death and sudden birth of entanglement are observed, while the peak value of quantum discord is reached periodically. The results of our investigation also suggest that some special quantum state with non-zero quantum discord may be created.     

Electromagnetic interactions in liquid helium

The Hamiltonian of interaction of liquid helium with the quantized electromagnetic field plays an important role in such phenomena as Raman scattering, excitons, and possible cooperative effects of exchange of virtual photons. This interaction has been derived from first principles by application of an appropriate unitary transformation to the second-quantized Hamiltonian of nuclei and electrons interacting with the quantized radiation field. The transformation is chosen so that the atomic bound states appear explicitly in the relevant scattering and reaction terms of the transformed Hamiltonian.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

Nonlinear properties of gated graphene in a strong electromagnetic field

We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.     

Dynamics of the Two Atoms Interacting with Quantized Two Modes Cavity Fields in the Ladder Configuration

Exact solutions are obtained for the collective model of two identical two level atoms interacting with a quantized bimodal-field in a lossless cavity. A unitary transformation method is used to solve the time-dependent problem, that also gives the eigensolutions of the interacting Hamiltonian. In particular, we study the atomic population dynamics and the dynamics of the photon statistics in the two cavity modes. We present evidence of co-operative effects.     

嵌入并联耦合双量子点介观环系统中的近藤效应

使用双杂质Anderson模型的哈密顿，从理论上研究了一个嵌入并联耦合双量子点介观环系统 , 当处在Kondo区时的基态性质, 并用slave-boson平均场方法求解了哈密顿.研究的结果表 明， 在这个系统中，当两个量子点处于强耦合时，两个量子点可以相干耦合成一个人造分 子，导致一个增强的Kondo效应和超强持续电流的出现.因此，在未来的纳米装置应用中，这 个系统具有潜在的应用价值. 关键词： 并联耦合双量子点 Kondo效应 超强持续电流     

光子晶格中光束演化的二能级模型及非线性Landau-Zener隧穿

推导了光束在Kerr介质、屏蔽介质及光伏介质的一维光子晶格中演化的二能级形式,给出了光束在这三种光折变介质中传播时二能级系统的经典哈密顿形式.以屏蔽介质为例,做出了空间相图,当非线性参数变化时,空间相图的拓扑改变.给出了空间相图的拓扑发生改变时,非线性参数的临界值.数值研究了非线性Landau-Zener（LZ）隧穿,得到非线性参数与LZ隧穿率的关系,发现非线性参数大于0时增强了隧穿,而非线性参数小于0时抑制了隧穿. 关键词： 二能级模型 光折变介质 光子晶格 非线性Landau-Zener隧穿     

Landau-Zener Tunneling for Dephasing Lindblad Evolutions

We consider a family of time-dependent dephasing Lindblad generators which model the monitoring of the instantaneous Hamiltonian of a system by a Markovian bath. In this family the time dependence of the dephasing operators is (essentially) governed by the instantaneous Hamiltonian. The evolution in the adiabatic limit admits a geometric interpretation and can be solved by quadrature. As an application we derive an analog of the Landau-Zener tunneling formula for this family.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.     

Many-particle quantum theory for a class of free-electron devices

The small signal, cold beam regime of a wide class of free-electron lasers including magnetic and optical helical wigglers and stimulated Cerenkov radiation is discussed based on the many-particle fully quantized Bambini-Renieri Hamiltonian. The central topic is the photon statistics under various conditions and the significance of cooperative effects.     

Quantum Aspects of the Fundamental Dirac Membrane Model

The classical relativistic Hamiltonian derived by Dirac for a charged membrane is written in a linearized form and it is pointed out that the membrane has spin 1/2 under the action of an external magnetic field. A spin-rotation coupling term is included into the linearized Hamiltonian and the corresponding wave equation for the membrane is written. It leads to quantized radial modes of oscillations and its first eigenvalues are derived numerically. Asymptotic solutions are also considered.     

介观互感耦合阻尼LC并联电路的量子化能谱

对介观互感耦合阻尼并联LC电路作双模耦合阻尼谐振子处理,将其量子化,通过三次幺正变换,将体系的哈密顿量对角化,在此基础上给出了体系的能谱。     

Giant Kondo Resonance of Parallel-Coupled Double Quantum Dots Embedded in an A-B Ring

We theoretically study the properties of the ground state of the parallel-coupled double quantum dots embedded in a mesoscopic ring in the Kondo regime by means of the two-impurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. We find that in this system, the persistent current depends sensitively on both the parity of this system and the size of the ring. In the strong coupling regime, the giant sharp current peak appears, at the same time, the parity dependence of the persistent current disappears. These imply that in the strong coupling regime, there exists giant Kondo resonance and the two dots can be coupled coherently. Thus this system might be a candidate for future device applications.     

Exact solution of the ion‐laser interaction in all regimes

We show that in the trapped ion‐laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb‐Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.     

THE QUANTIZATION OF A FOURTH-ORDER EQUATION WITHOUT A SECOND-ORDER LAGRANGIAN

We present an equation of the fourth-order which does not possess a second-order Lagrangian and demonstrate by means of the method of reduction of order that one can obtain a first-order Lagrangian for it. This opens the way to quantization through the construction of an Hamiltonian which is suitable to be quantized according to the procedure of Dirac with the correct physical attributes.     

On local and global currents in mesoscopic conductors

Using linear response theory we show that, in a quasi-stationary state, the local multiprobe conductance of a mesoscopic system of non-interacting electrons with a time reversal invariant Hamiltonian does not depend on the local shape of the driving self-consistent potential and thus is entirely determined by the asymptotic values of the potential in the leads. In the ballistic limit, the local conductance in the lateral direction exhibits oscillations depending on the occupation of channels. Scattering by a point impurity leads to softening of the quantized global conductance steps. In addition to that for an attractive scattering potential, a dip occurs in each plateau regime the shape of which is calculated for different values of the potential strength. We also investigate the local conductance for both a point scatterer and a finite scattering region.     

嵌入耦合量子点的介观Aharonov-Bohm环内的持续电流

使用双杂质的Anderson模型的哈密顿量，从理论上研究了一个嵌入耦合量子点的介观Aharonov-Bohm环系统处在Kondo区时的基态性质, 并用slave-boson平均场方法求解了哈密顿量. 结果表明, 在这个系统中, 宇称效应和复杂的电流 相位关系的出现反映了两个量子点可以相干耦合. 关键词： 持续电流 耦合量子点 宇称效应 Kondo效应     

Entanglement dynamics of a strongly driven trapped atom

We study the entanglement between the internal electronic and the external vibrational degrees of freedom of a trapped atom which is driven by two lasers into electromagnetically induced transparency. It is shown that basic features of the intricate entanglement dynamics can be traced to Landau-Zener splittings (avoided crossings) in the spectrum of the atom-laser field Hamiltonian. We further construct an effective Hamiltonian that describes the behavior of entanglement under dissipation induced by spontaneous emission processes. The proposed approach is applicable to a broad range of scenarios for the control of entanglement between electronic and translational degrees of freedom of trapped atoms through suitable laser fields.     

Equality of the Bulk and Edge Hall Conductances in a Mobility Gap

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic. An erratum to this article is available at .