Exact solution of an integrable quantum spin chain with competing interactions

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T-Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.     

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schr?dinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.     

Electron spectrum in a quantum superlattice with cylindrical symmetry

A quantum superlattice with axial symmetry, a heterostructure in which two semiconductor materials in the form of coaxial wires with a nanosize cross section are in contact with one another and form a periodic structure in the radial direction, is studied. It is shown that the electron energy spectrum consists of alternating allowed and forbidden bands. The electron dispersion law is studied for different values of the period of the potential, thicknesses of the semiconductor layers, and radius of the inner crystal of the system. It is shown that the coherent electron effective mass of the quantum superlattice is a tensor: The longitudinal component is close in value to the electron effective mass of the semiconductor material characterizing the quantum well of the superlattice and the radial component depends strongly on the period of the potential, the thicknesses of the coaxial semiconductor layers, and the core radius of the heterosystem, taking on positive or negative values in different allowed bands. Fiz. Tverd. Tela (St. Petersburg) 40, 557–561 (March 1998)     

Ratchet effects in quantum wells with a lateral superlattice

Experimental and theoretical works on the ratchet effects in quantum wells with a lateral superlattice excited by alternating electric fields of terahertz frequency range has been reviewed. We discuss the Seebeck ratchet effect and helicity driven photocurrents and show that the photocurrent generation is based on the combined action of a spatially periodic in-plane potential and a spatially modulated light.     

Electric-field effect on shallow impurity ground state in nanowire superlattice

We have developed a variational formalism to analyze the effect of electric field on the donor ground state in a nanowire superlattice with cylindrical cross-section. The trial function is taken as a product of the free-electron ground state wave function with an envelope function that is a solution of a differential equation arising from the Schrödinger variational principle. We establish a close relationship between the donor ground state energy and density of charge induced by the unbound electron at the point of donor location. Also, we show that electric field applied along the crystal growth direction can easily shift the peak position of the free-electron density distribution from the central well toward one of the nanowire ends, providing a variation of the average electron-ion separation and a considerable alteration of the donor ground state energy.     

Spectrum of an electron in a superlattice along a cylindrical quantum wire

The quasi-one-dimensional superlattice of two contacting semiconductor materials along a cylindrical quantum wire (using the example of CdS/HgS) is investigated. It is shown that the energy center of the electron is an alternation of allowed and forbidden bands. The dispersion law for different values of the period of the potential and the radius of the quantum wire is investigated. A transition to the Kronig-Penney model is obtained. The effective masses of the electrons of different bands are found. Chernovits State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 96–103, February, 1998.     

Electric-field effects on photoluminescence properties in a GaAs/AlAs marginal type-I superlattice

We have investigated the electric-field effects on the cw and time-resolved photoluminescence (PL) properties in a marginal type-I GaAs/AlAs superlattice (SL) whose lowest X state (X₁) is situated in the lowest Γ(Γ₁) miniband. In the low bias voltage regime, the PL spectra reveal the transition between type-I and type-II radiative recombination processes caused by Wannier–Stark localization. In contrast, in the high bias voltage regime, the decay time of the time-resolved PL is prolonged. This is because of delayed carrier transport caused by Γ–X transfer. From these results, it was found that marginal type-I SLs present various interesting phenomena that originate from the competitive carrier transport among the Γ miniband, the localized Γ Stark–ladder states, and the X₁ state.     

Exact solution for particle trajectories in modified quantum mechanics

Considering a simple quantum master equation for a free particle we prove that after a given period of relaxation the solutions can be interpreted exactly in terms of uniform localized wave packets whose centers imitate classical trajectories.     

Exact solution of the two-mode quantum Rabi model

An analytical method is developed to study the two-mode quantum Rabi model. For certain specific parameter conditions, especially for the resonant conditions, we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies. It is shown that there exist new types of the exact energies which do not correspond to the level-crossings. Our analytical method may find applications in some related models.     

Exact solution of a topological spin ring with an impurity

The spin-1/2 Heisenberg chain coupled to a spin-S impurity moment with anti-periodic boundary condition is studied via the off-diagonal Bethe ansatz method. The twisted boundary breaks the U(1) symmetry of the system, which leads to that the spin ring with impurity can not be solved by the conventional Bethe ansatz methods. By combining the properties of the R-matrix, the transfer matrix, and the quantum determinant, we derive the T –Q relation and the corresponding Bethe ansatz equations. The residual magnetizations of the ground states and the impurity specific heat are investigated. It is found that the residual magnetizations in this model strongly depend on the constraint of the topological boundary condition, the inhomogeneity of the impurity comparing with the hosts could depress the impurity specific heat in the thermodynamic limit. This method can be expand to other integrable impurity models without U(1) symmetry.     

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on “pair propagation through a vertex”. The Bethe ansatz-type equations obtained reduce, in the case of lattice size N = 1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.     

Effective-mass superlattice as an injector in quantum cascade lasers

In this paper, we have developed new design of the injector for quantum cascade structures based on the effective mass superlattice. The transmission spectra of the conventional injector and effective-mass injector have been compared. Advantage of the effective-mass injector is more uniform spectrum of pass-band. This feature allows to improve controllability of the quantum cascade laser, to increase stability of its operation and to decrease sensitivity to noise in applied voltage bias. Also, we have computed geometrical parameters for effective-mass injector which is appropriate to provide inverted population in existing quantum-cascade lasers. Such injector should be characterized by 15–25 numbers of layers with widths of layers up to 2 nm.     

Exact solution of quantum gravity in 1 + 1 dimensions

Quantum gravity in 1 + 1 dimensions, with zero cosmological constant is formulated, including contributions from all possible topologies. The spectrum and the S-matrix are calculated exactly. Pure gravity is found to exist in a disordered phase, dominated by topologically non-trivial configurations. In the presence of fermionic matter fields, space-time can undergo a phase transition to an ordered phase.     

Exact solution for an open universe with viscosity

The derivation of exact cosmological solutions describing an open universe with a conformally flat metric and volume viscosity is discussed. The method used in the article permits the modeling of an open universe to be reduced to the problem of mechanical motion of a particle in a specified force field. The behavior of the equation of state, which changes as the universe evolves, is investigated. A new exact solution of the gravitation equations is found in a simple form corresponding to an equivalent, variable-frequency oscillator with linear damping.This work has been performed under the auspices of the Astronomy Joint Scientific and Engineering Program.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 79–83, January, 1995.     

Compression of terahertz radiation in resonant systems with a quantum superlattice

It is shown theoretically that ultrashort terahertz electromagnetic pulses can be generated in resonant systems containing a quantum semiconductor superlattice. This effect is due to the compression of radiation incident on a cavity as a result of ultrafast self-modulation of the cavity Q factor upon cyclic switching of the superlattice from the screening to the transparent state in a pump field.     

Exact results for the persistent current in an aharonov-bohm ring with a quantum impurity

We consider the problem of a persistent current in a one-dimensional mesoscopic ring with the electrons coupled by a spin exchange to a magnetic impurity. We show that this problem can be mapped onto an integrable model with a quadratic dispersion (with the latter property allowing for an unambiguous definition of the persistent current). We have solved the model exactly by a Bethe ansatz and found that the current is insensitive to the presence of the impurity. We conjecture that this result holds for any integrable quantum impurity model with an electronic dispersionε(k) that is an even function ofk.     

Angular distribution of electrons injected through a quantum point contact

This paper reports on the measurement of the angular distribution of electrons injected through a quantum point contact. We observed double peaks in the distribution with the point contact quantized in two modes. Our calculation of the distribution using an approximation of Fraunhofer diffraction through a quantized single slit agreed well with results. This paper also discusses the interference between the first and second modes, and shows how the terms of interference in the angular distribution are canceled.