Quantum groups of fermionic algebras

We consider inhomogeneous quantum groups that transform various types of fermions: standard fermions, commuting fermions and orthofermions. These quantum groups are notq-deformations.     

On the Structure of Inhomogeneous Quantum Groups

We investigate inhomogeneous quantum groups G built from a quantum group H and translations. The corresponding commutation relations contain inhomogeneous terms. Under certain conditions (which are satisfied in our study of quantum Poincaré groups [12]) we prove that our construction has correct ‘size’, find the R-matrices and the analogues of Minkowski space for G. Received: 3 April 1995 / Accepted: 23 September 1996     

The inhomogeneous invariance quantum supergroup of supersymmetry algebra

We consider an inhomogeneous quantum supergroup which leaves invariant a supersymmetric particle algebra. The quantum sub-supergroups of this inhomogeneous quantum supergroup are investigated.     

Solutions of Klein-Gordon and Dirac equations on quantum Minkowski spaces

Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they have the same dimensions as in the classical case. Formal solutions of the corresponding Klein-Gordon and Dirac equations are found. The Fock space construction is sketched.This research was supported in part by NSF grant DMS-9508597 and in part by Polish KBN grant No. 2 P301 02007.     

The Inhomogeneous Invariance Quantum Group of?Particle Algebras with Continuous Parameters

We construct the inhomogeneous quantum groups with continuous parameters which leave the boson and fermion algebras of field theory invariant.     

Projective representations of the inhomogeneous Hamilton group: Noninertial symmetry in quantum mechanics

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries include the Weyl–Heisenberg group; the hermitian representations of its algebra are the Heisenberg commutation relations that are a foundation of quantum mechanics. The Weyl–Heisenberg group is a one dimensional central extension of the abelian group and its unitary representations are therefore a particular projective representation of the abelian group of translations on phase space. A theorem involving the automorphism group shows that the maximal symmetry that leaves the Heisenberg commutation relations invariant is essentially a projective representation of the inhomogeneous symplectic group. In the nonrelativistic domain, we must also have invariance of Newtonian time. This reduces the symmetry group to the inhomogeneous Hamilton group that is a local noninertial symmetry of the Hamilton equations. The projective representations of these groups are calculated using the Mackey theorems for the general case of a nonabelian normal subgroup.     

Quantum hall effect in inhomogeneous media: Effective characteristics and local current distribution

An analysis is made of the problem of current flow in heterophase inhomogeneous media in the quantum Hall effect regime. Duality relations are derived and expressions are obtained for the effective conductivity of inhomogeneous media over the entire range of concentrations. Local current distributions (fields) are determined in the quantum Hall effect regime.     

Interplay between Zeeman coupling and swap action in spin-based quantum computer models: error correction in inhomogeneous magnetic fields

We consider theoretically the interplay between Zeeman coupling and exchange-induced swap action in spin-based quantum dot quantum computer models in the presence of inhomogeneous magnetic fields, which are invariably present in real systems. We estimate quantitatively swap errors caused by the inhomogeneous field, establishing that error correction would, in principle, be possible in the presence of nonuniform magnetic fields in realistic structures.     

海森堡XYZ自旋链系统的热纠缠与局域量子不确定性研究

研究了热平衡温度,自旋交换相互作用,Dzyaloshinskii-Moriya(DM)相互作用及外加非一致性磁场对两比特海森堡XYZ自旋链量子系统的热纠缠与局域量子不确定度的影响,对比分析了并发度量子纠缠与局域量子不确定度描述自旋链系统量子关联的差别.结果表明自旋链系统的量子纠缠在热平衡温度,DM相互作用及外加磁场的非一致性参数的变化情况下均会出现纠缠突然死亡的再生现象,而自旋链系统的局域量子不确定度随着这些参数呈连续变化现象.并且,自旋交换相互作用,DM相互作用及外加横向磁场作用强度较小时,他们的变化对自旋链系统的量子纠缠与局域量子不确定度的影响有着明显的差别.     

Linear quantum enskog equation II. Inhomogeneous quantum fluids

This is the second part of a work concerned with the quantum-statistical generalization of classical Enskog theory, whereby the first part is extended to spatially inhomogeneous fluids. In particular, working with Liouville operators and using cluster expansions and projection operators, we derive the inhomogeneous linear quantum Enskog equation and express the dynamic structure factor and the nonlocal mobility tensor in terms of the corresponding quantum Enskog collision operator. Thereby static correlations due to excluded volume effects and quantum-statistical correlations due to the fermionic (bosonic) character of the pairwise strongly interacting particles are treated exactly. When static correlations are neglected, this Enskog equation reduces to the inhomogeneous linear quantum Boltzmann equation (containing an exchange-modifiedt-matrix). In the classical limit, the well-known linear revised Enskog theory is recovered for hard spheres.     

Quantum Dot Versus Quantum Well Semiconductor Optical Amplifiers for Subpicosecond Pulse Amplification

The performance of quantum well and quantum dot semiconductor optical amplifiers was theoretically investigated. The effects on subpicosecond pulse propagation due to gain and refractive index dispersion, calculated using a microscopic polarization equation and a reduced wave equation in the linear regime including the background refractive index dispersion, were used in the comparison. In particular, the spectral shift and phase modulation imposed on the pulse were compared. It is shown that quantum dot amplifiers suffer comparable spectral shifts to the quantum well amplifier, strong linear frequency chirp and large pulse broadening. In quantum dot amplifiers with small inhomogeneous broadening, similar pulse break-up is shown as that calculated for the quantum well amplifier. In quantum dot amplifiers with large inhomogeneous broadening, the background refractive index dispersion makes the linear frequency chirp the dominant feature. In the light of our calculations, the advantages and disadvantages of quantum dot and quantum well amplifiers are discussed.     

Quasi-1 structure on q-Poincaré algebras

We use braided groups to introduce a theory of 1-structures on general inhomogeneous quantum groups, which we formulate as quasi-1 Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix from appropriate to the previous q-Euclidean and q-Minkowski space-time algebras R₂₁x₁x₂ = x₂x₁R and R₂₁u₁Ru₂ = u₂R₂₁u₁R. We obtain unitarity of the fundamental differential representations. We further show that the Euclidean and Minkowski-Poincaré quantum groups are twisting equivalent by another quantum cocycle.     

q-deformed path integral

Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)_q, we construct the path integral representation for the quantum mechanical evolution operator kernel of the q-oscillator.     

Quantum teleportation via a two-qubit Heisenberg <Emphasis Type="Italic">XXZ</Emphasis> chain – effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.     

Modeling and analysis of the effects of inhomogeneous carrier distributions in InGaN multiple quantum wells

It is well known that carrier distribution in InGaN multiple quantum wells (MQWs) can be significantly inhomogeneous. However, the conventional ABC recombination model assumes that carriers are uniformly distributed throughout the MQW. In this paper, a modified ABC model that considers the unequal carrier density in the QWs was developed. From the analysis of the developed ABC model, the effective recombination coefficients and modified internal quantum efficiency (IQE) were obtained for an arbitrary carrier distribution in MQWs. The efficiency droop was found to be aggravated as the carrier distribution was increasingly inhomogeneous. However, it was also found that the effect of inhomogeneous carrier distribution alone was not sufficient to explain the IQE droop with the theoretical Auger recombination coefficient based on indirect Auger processes. The developed ABC model is expected to provide insight into the influence of inhomogeneous carrier distributions in MQWs on the efficiency droop in GaN-based light-emitting diodes.     

Collective modes of quantum dot ensembles in microcavities

Emission spectra of quantum dot arrays in zero-dimensional microcavities are studied theoretically. It is shown that their form is determined by the competition between collective superradiant mode formation and inhomogeneous broadening. A random sources method is used to calculate the photoluminescence spectra from an nonresonant pumped microcavity, and a standard diagram technique is used to provide a microscopic justification for the random sources method. The emission spectra of a microcavity are analyzed taking into account the spread of exciton energy due to inhomogeneous distribution of quantum dots and tunneling between them. It is demonstrated that the luminescence spectra of strongly tunnel-coupled quantum dots are sensitive to the dot positions, and the collective mode can (under certain conditions) be stabilized by random tunneling links.     

Determining the orientation of single quantum systems by means of scanning fluorescence microscopy

It shown via computational methods that the orientation and coordinates of single quantum electric dipole emitters in an isotropic medium can be clearly determined from scanned confocal luminescent images acquired using a circular inhomogeneous incoming beam. The efficiencies of circular inhomogeneous and radial beams are compared.     

Quantum Incompressibility of a Falling Rydberg Atom, and a Gravitationally-Induced Charge Separation Effect in Superconducting Systems

Freely falling point-like objects converge toward the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum mechanical object such as a hydrogen atom prepared in a high principal-quantum-number state, i.e. a circular Rydberg atom, is predicted to fall more slowly than a classical point-like object, when both objects are dropped from the same height above the Earth’s surface. This indicates that, apart from transitions between quantum states, the atom exhibits a kind of quantum mechanical incompressibility during free fall in inhomogeneous, tidal gravitational fields like those of the Earth.     

An Analog of the Kubo formula for conductivity of spatially inhomogeneous media in spatially inhomogeneous electric fields

The average densities of currents and charges induced by a weak electromagnetic field in spatially inhomogeneous systems at a finite temperature are calculated. The Kubo formula for the electrical conductivity tensor is generalized to spatially inhomogeneous systems and spatially inhomogeneous fields. The contributions containing electric fields and derivatives of the fields with respect to coordinates are separated. It is shown that semiconductor quantum wells, wires, and dots can be treated as spatially inhomogeneous systems.     

Drift vortices in inhomogeneous collisional dusty magnetoplasma

For the sake of investigating the drift coherent vortex structure in an inhomogeneous dense dusty magnetoplasma,using the quantum hydrodynamic model a nonlinear controlling equation is deduced when the collision effect is considered.New vortex solutions of the electrostatic potential are obtained by a special transformation method, and three evolutive cases of monopolar vortex chains with spatial and temporal distribution are analyzed by representative parameters. It is found that the collision frequency, particle density, drift velocity, dust charge number, electron Fermi wavelength, quantum correction,and quantum parameter are all influencing factors of the vortex evolution. Compared to the uniform dusty system, the vortex solutions of the inhomogeneous system present richer spatial evolution and physical meaning. These results may explain corresponding vortex phenomena and support beneficial references for the dense dusty plasma atmosphere.