Inhomogeneous quantum diffusion of muons in solids

This article deals with the problems raised when a muon(muonium) quantum diffusion in a crystal is highly inhomogeneous. It is shown how static disorder arising from the crystal doping influence the diffusion process and drastically changes both the time decay of the polarization function and the temperature dependence of the depolarization rate. The spin depolarization of muons moving in a spatially inhomogeneous defect potential and trapping of particles by the long-ranged traps is studied in detail. Most attention is given to the particle localization and delocalization phenomena resulting in the two-component behavior of muon polarization at low temperature. Finally, the experimental data on muon depolarization in insulators KCl, GaAs, N₂ and superconducting metals Al, V are analyzed.     

Current oscillations in a double quantum well during quasistationary state decay

Temporal current oscillations in a double quantum well caused by interference of the wave functions of quasistationary states are considered. An algorithm and results of calculations of the spectral function of the system and time dependences of the probability of particle localization in the double well and of the current in the well are presented.     

Inhomogeneous quantum groups

Inhomogeneous quantum groups corresponding to the homogeneous quantum groupsU _q (N), SO _q (N) and theq-deformed Lorentz group acting on affine quantum spaces are constructed. Special representations of the translation part are investigated.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June, 1992.     

Inhomogeneous quantum groups

Inhomogeneous quantum groups corresponding to the homogeneous quantum groupsU _q (N), SO _q (N) and theq-deformed Lorentz group acting on affine quantum spaces are constructed.     

Solid state NMR free induction decay in the presence of vacancy diffusion

A theoretical calculation of the NMR free induction decay (FID) of spins in a periodic lattice is given where the spin-spin interaction is dipolar and where account is taken of vacancy motion. The expansion of the FID to any order is exact which allows for the inclusion of effects arising from nearest neighbor and next nearest neighbor (τ_NN and τ_NNN) hopping times. It is shown that expansion of the FID to terms of order t⁴ allows for the separate determination of τ_NN and τ_NNN.     

The quasiclassical Langevin equation and its application to the decay of a metastable state and to quantum fluctuations

We report on investigations on the consequences of the quasiclassical Langevin equation. This Langevin equation is an equation of motion of the classical type where, however, the stochastic Langevin force is correlated according to the quantum form of the dissipation-fluctuation theorem such that ultimately its power spectrum increases linearly with frequency. Most extensively, we have studied the decay of a metastable state driven by a stochastic force. For a particular type of potential well (piecewise parabolic), we have derived explicit expressions for the decay rate for an arbitrary power spectrum of the stochastic force. We have found that the quasiclassical Langevin equation leads to decay rates which are physically meaningful only within a very restricted range. We have also studied the influence of quantum fluctuations on a predominantly deterministic motion and we have found that there the predictions of the quasiclassical Langevin equations are correct.     

Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field

We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in nay number of dimensions,d. We prove that in the ground state the power law correction to the exponential decay of the two point function isd/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d-1)/2 becomesd/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Fröhlich [5].     

Remote state preparation of a photonic quantum state via quantum teleportation

We demonstrate an experimental realization of remote state preparation via the quantum teleportation algorithm, using an entangled photon pair in the polarization degree of freedom as the quantum resource. The input state is encoded on the path of one of the photons from the pair. The improved experimental scheme allows us to control the preparation and teleportation of a state over the entire Bloch sphere with a resolution of the degree of mixture given by the coherence length of the photon pair. Both the preparation of the input state and the implementation of the quantum gates are performed in a pair of chained displaced Sagnac interferometers, which contribute to the overall robustness of the setup. An average fidelity above 0.9 is obtained for the remote state preparation process. This scheme allows for a prepared state to be transmitted on every repetition of the experiment, thus giving an intrinsic success probability of 1.     

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-¹⁴N₂) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T ₁ ^–1 ) and transverse (T ₂ ^–1 ) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

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.     

The crossover from classical to quantum behavior in Duffing oscillator based on quantum state diffusion

The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one.     

Stochastic processes of a quantum state

Starting from a quantum state represented by its wave function (x), satisfying the Schrödinger equation, we determine stochastic processes which provide the same time evolution for the probability density(x)=¦(x)¦². The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.     

Remark on the decay of a mixed state

Czechoslovak Journal of Physics - The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for...     

Inhomogeneous quantum groups and their quantized universal enveloping algebras

The quantum group IGL _q (N), the inhomogenization of GL _q (N), is formulated with -matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space.     

Free-induction decay in quantum wires

Using the time-dependent perturbation treatment, we report the occurrence of first-order free-induction decay in GaAs/GaAlAs quantum wire structures. The results of the theoretical investigation reveal oscillations in the decay profile of the polarization. The transient transmitted intensity has been found to decay in a time comparable to the inhomogeneous broadening time, which is much shorter than the dephasing time. We have also studied the transmitted intensity as a function of wire width and found the results to be in good qualitative agreement with that available in the literature.