Bihamiltonian structures and Stäckel separability

It is shown that a class of Stäckel separable systems is characterized in terms of a Gel’fand–Zakharevich bihamiltonian structure. This structure arises as an extension of a Poisson–Nijenhuis structure on phase space. It is also shown that the Casimir of the Gel’fand–Zakharevich bihamiltonian structure provides the family of commuting Killing tensors found by Benenti and that, because of Eisenhart’s theorem, characterize orthogonal separability. It is also shown that recently found properties of quasi-bihamiltonian systems are natural consequences of the geometry of the extension of the Poisson–Nijenhuis structure.     

Separable quantizations of Stäckel systems

In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2n$2n$ dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations–parametrized by n$n$ arbitrary functions–that turn this system into a quantum separable Stäckel system.     

A new integrable system on the sphere and conformally equivariant quantization

Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi–Moser system, we disclose a novel integrable system on the sphere Sⁿ$S^n$, namely the dual Moser system. The latter falls, along with the Jacobi–Moser and Neumann–Uhlenbeck systems, into the category of (locally) Stäckel systems. Moreover, it is proved that quantum integrability of both Neumann–Uhlenbeck and dual Moser systems is ensured by means of the conformally equivariant quantization procedure.     

A note on pseudo-Hermitian systems with point interactions and quantum separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.     

Remarks on separability of compound quantum systems and time reversal

A separability test for density matrices of compound quantum systems proposed recently by Peres is formulated in a manifestly basis independent way using antiunitary operators. We prove that the test amounts to a criterion for pure states, while it is known to fail to do so in the case of mixed states. An interesting connection with the operation of time reversal is thus exhibited.     

A sufficient and necessary criterion for separability of bipartite quantum states

A sufficient and necessary criterion for separability of bipartite quantum states is presented. We construct a class of mixed states in 2 ? k quantum systems and in 3 ? k quantum systems, respectively and show that these states are separable if and only if they are positive partial transpositions.     

The minimal length uncertainty and the quantum model for the stock market

We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the fourth power of the trend. We study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system. The connection between the information frequency and the transition probabilities is discussed finally.     

Schrieffer–Wolff transformation for quantum many-body systems

The Schrieffer–Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to . We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the nth-order effective Hamiltonian approximates the exact ground state energy.     

Partial quantum recurrence in free and quasibound systems

The quantum motion of a periodically two-sided kicked free particle is studied under various boundary conditions. The quasienergies, quasistates and the energy of the system are determined exactly. It is found that the energy of the system recurs irrespective of boundary conditions whereas the wave function shows recurrence only for a completely bound particle.     

From classical mechanics with doubled degrees of freedom to quantum field theory for nonconservative systems

The 2×2$2\times 2$-matrix structure of Green?s functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton?s principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley?s Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.     

Simple theoretical analysis of the Einstein’s photoemission from quantum confined superlattices

In this paper, we study the Einstein’s photoemission from III–V, II–VI, IV–VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.     

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.     

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.     

Reduced dynamics and the master equation of open quantum systems

An exact reduced density operator of a quantum system interacting with a bosonic thermal reservoir is derived by means of the simple algebraic method. The necessary and sufficient condition is found that the time-convolutionless master equation becomes exact up to the second order with respect to the system-reservoir interaction. The result is examined by means of the boson-detector model. The reduced dynamics of a quantum system interacting with a classical reservoir is also discussed.     

Far-infrared spectroscopy of quantum wires and dots, breaking Kohn’s theorem

We review far-infrared experiments on quantum wires and dots. In particular, we show that with tailored deviations from a parabolic external lateral confinement potential one can break Kohn’s theorem. This allows a detailed investigation of the internal relative motion in quantum dots and wires and the study of electron–electron interaction effects, for example, the formation of compressible and incompressible states in quantum dots and antidots.     

Properties of narrow gap quantum dots and wells in the InAs/InSb/GaSb systems

The properties of InSb quantum dots grown by metal organic vapour phase epitaxy are summarised as deduced from photoluminescence, magneto-photoluminescence, and far-infrared modulated photoluminescence experiments. A technique is described for shifting the emission of these dots to lower energy by coupling them with a narrow InAs quantum well, leading to the demonstration of electroluminescence at 2.3 μm.     

Geometric phases and the informational completeness of quantum frames

The basic results on geometric phases are rederived by using infinite dimensional coordinate charts in line bundles, in Hopf bundles, and in projective Hilbert spaces. The determination of a quantum state can be then geometrically described as the measurement of Fubini-Study distances from that state to the elements of informationally complete quantum frames. The basic geometric features of such quantum frames are formulated, and their relationships to corresponding classical frames are analyzed.     

压缩真空态中原子与场的量子纠缠和量子discord

在压缩真空库中,研究了原子与场的相互作用下二比特体系的量子discord和量子纠缠的动力学行为.重点分析了原子的初始态系数和压缩真空库的压缩系数对量子纠缠和量子discord的影响.通过数值分析我们得到,随着原子的初始态系数和压缩真空库的压缩系数值的增加,量子纠缠和量子discord都会减小,但量子纠缠比量子discord减小的更快一些.最后研究了在原子的初始态系数和压缩真空库的压缩系数的值相同的情况下,量子discord比量子纠缠存在的时间更长些.     

Raman study of Si–Ge intermixing in Ge quantum rings and dots

The Ge/Si (1 0 0) nanostructures have been studied by atomic force microscopy (AFM) and Micro Raman optical spectroscopy. Two layers of Ge of total thickness 0.75 nm and Si cap with thickness 2.5 nm were deposited by the method of molecular beam epitaxy at the temperature range 640–700 °C. AFM shows both quantum dots and ring-shape Ge nanostructures. From the analysis of the intensity and energy shift of the Raman signal we have found that the average concentration of Ge decreases considerably from 44% to 27%, when the growth temperature increases, whereas the degree of strain relaxation remains roughly the same. This allows us to conclude that intermixing is a dominating mechanism for strain relaxation in processes of transformation of Ge quantum dots to quantum rings.     

Material parameters of InGaAsP and InAlGaAs systems for use in quantum well structures at low and room temperatures

The set of material parameters for quantum well structures is of immense importance because of its usage in the development of theories, extraction of experimental data, and the proper design of devices. In particular, the (Al,In)GaAs/GaAs, InGaAs/InP and (In,Ga)AlAs/InGaAs quantum well systems have drawn a lot of attention. They form the center core of materials used for fundamental basic research and device applications. Despite the presence of some review articles and reference books, there is a lack of clear reference on the accurate determination of the material parameters for quantum wells. This review aims to provide a comprehensive and systematic set of material parameters for the above quantum well systems grown on (1 0 0) substrates at two different temperatures, below 10 K and at around 300 K. The parameters are compared against experimental data from various fabrication sources, measurement techniques, and quantum well structures. The values presented here serve as an accurate and up to date source of reference.