On the Lagrangian Realization of the WZNW Reductions

We develop a phase space path-integral approach for deriving the Lagrangian realization of the models defined by Hamiltonian reduction of the WZNW theory. We illustrate the uses of the approach by applying it to the models of non-Abelian chiral bosons, $W$-algebras and the GKO coset construction, and show that the well-known Sonnenschein's action, the generalized Toda action and the gauged WZNW model are precisely the Lagrangian realizations of those models, respectively.Comment: 15 pages, DIAS-STP-92-09/UdeM-LPN-TH-92-9

Global Aspects of the WZNW Reduction to Toda Theories

It is well-known that the Toda Theories can be obtained by reduction from the Wess-Zumino-Novikov-Witten (WZNW) model, but it is less known that this WZNW $\rightarrow$ Toda reduction is \lq incomplete'. The reason for this incompleteness being that the Gauss decomposition used to define the Toda fields from the WZNW field is valid locally but not globally over the WZNW group manifold, which implies that actually the reduced system is not just the Toda theory but has much richer structures. In this note we furnish a framework which allows us to study the reduced system globally, and thereby present some preliminary results on the global aspects. For simplicity, we analyze primarily 0 $+$ 1 dimensional toy models for $G = SL(n, {\bf R})$, but we also discuss the 1 $+$ 1 dimensional model for $G = SL(2, {\bf R})$ which corresponds to the WZNW $\rightarrow$ Liouville reduction.Comment: 22 pages, INS-Rep.-104

Classical Aspects of Quantum Walls in One Dimension

We investigate the system of a particle moving on a half line x >= 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering with the quantum wall, and also by examining the WKB-exactness of the transition kernel based on the regularized potentials. It is shown that no classical counterpart exists for walls with L < 0, and that the WKB-exactness can hold only for L = 0 and L = infinity.Comment: TeX, 21 pages, 4 figures. v2: some parts of the text improved, new and improved figure

Quantization of a relativistic particle on the SL(2,R) manifold based on Hamiltonian reduction

A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the reduced system into two coadjoint orbits of the group. We find that the Hilbert space consists of states given by the discrete series of the unitary irreducible representations of SL(2,R), and with a positive-definite, discrete spectrum.Comment: 12 pages, INS-Rep.-104

Spin-torque efficiency enhanced by Rashba spin splitting in three dimensions

We examine a spin torque induced by the Rashba spin-orbit coupling in three dimensions within the Boltzmann transport theory. We analytically calculate the spin torque and show how its behavior is related with the spin topology in the Fermi surfaces by studying the Fermi-energy dependence of the spin torque. Moreover we discuss the spin-torque efficiency which is the spin torque divided by the applied electric current in association with the current-induced magnetization reversal. It is found that high spin-torque efficiency is achieved when the Fermi energy lies on only the lower band and there exists an optimal value for the Rashba parameter, where the spin-torque efficiency becomes maximum.Comment: 7 pages, 5 figure

Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction

The Schroedinger operator with point interaction in one dimension has a U(2) family of self-adjoint extensions. We study the spectrum of the operator and show that (i) the spectrum is uniquely determined by the eigenvalues of the matrix U belonging to U(2) that characterizes the extension, and that (ii) the space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius strip with boundary. We employ a parametrization of U(2) that admits a direct physical interpretation and furnishes a coherent framework to realize the spectral duality and anholonomy recently found. This allows us to find that (iii) physically distinct point interactions form a three-parameter quotient space of the U(2) family.Comment: 16 pages, 2 figure

Spin-current absorption by inhomogeneous spin-orbit coupling

We investigate the spin-current absorption induced by an inhomogeneous spin-orbit coupling due to impurities in metals. We consider the system with spin currents driven by the electric field or the spin accumulation. The resulting diffusive spin currents, including the gradient of the spin-orbit coupling strength, indicate the spin-current absorption at the interface, which is exemplified with experimentally relevant setups.Comment: 13 pages, 5 figure

Quantum contact interactions

The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is identified.Comment: A lecture presented at the 2nd Winter Institute on Foundations of Quantum Theory and Quantum Optics (WINST02), Jan. 2-11, 2002, S.N.Bose Institute, Calcutta, India: 8 pages latex with Indian Acad. Sci. style fil