Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Theory of valley-orbit coupling in a Si/SiGe quantum dot

Electron states are studied for quantum dots in a strained Si quantum well, taking into account both valley and orbital physics. Realistic geometries are considered, including circular and elliptical dot shapes, parallel and perpendicular magnetic fields, and (most importantly for valley coupling) the small local tilt of the quantum well interface away from the crystallographic axes. In absence of a tilt, valley splitting occurs only between pairs of states with the same orbital quantum numbers. However, tilting is ubiquitous in conventional silicon heterostructures, leading to valley-orbit coupling. In this context, "valley splitting" is no longer a well defined concept, and the quantity of merit for qubit applications becomes the ground state gap. For typical dots used as qubits, a rich energy spectrum emerges, as a function of magnetic field, tilt angle, and orbital quantum number. Numerical and analytical solutions are obtained for the ground state gap and for the mixing fraction between the ground and excited states. This mixing can lead to valley scattering, decoherence, and leakage for Si spin qubits.Comment: 18 pages, including 4 figure

Density Functional Application to Strongly Correlated Electron Systems

The LSDA+U approach to density functional theory is carefully reanalyzed. Its possible link to single-particle Green's function theory is occasionally discussed. A simple and elegant derivation of the important sum rules for the on-site interaction matrix elements linking them to the values of U and J is presented. All necessary expressions for an implementation of LSDA+U into a non-orthogonal basis solver for the Kohn-Sham equations are given, and implementation into the FPLO solver is made. Results of application to several planar cuprate structures are reported in detail and conclusions on the interpretation of the physics of the electronic structure of the cuprates are drawn.Comment: invited paper in Journal of Solid State Chemistr

Investigations of Pairing in Anyon Systems

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attractive Aharonov-Bohm interaction is not sufficient to generate a gap in the Fermion spectrum.Comment: (11 pages, 2 Figures not included

Half-metallic ferromagnetism and structural stability of zincblende phases of the transition-metal chalcogenides

An accurate density-functional method is used to study systematically half-metallic ferromagnetism and stability of zincblende phases of 3d-transition-metal chalcogenides. The zincblende CrTe, CrSe, and VTe phases are found to be excellent half-metallic ferromagnets with large half-metallic gaps (up to 0.88 eV). They are mechanically stable and approximately 0.31-0.53 eV per formula unit higher in total energy than the corresponding nickel-arsenide ground-state phases, and therefore would be grown epitaxially in the form of films and layers thick enough for spintronic applications.Comment: 4 pages with 4 figures include

First-Principles Computation of YVO3; Combining Path-Integral Renormalization Group with Density-Functional Approach

We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t2g Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the ground state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods

New scenario for high-T_c cuprates: electronic topological transition as a motor for anomalies in the underdoped regime

We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, \delta=\delta_c, T=0, (n=1-\delta is an electron concentration) is at the origin of anomalous behaviour in the interacting system on one side of ETT, \delta<\delta_c. The most important is an appearance of the line of characteristic temperatures, T^*(\delta) \propto \delta_c-\delta. Application of the theory to high-T_c cuprates reveals a striking similarity to the observed experimentally behaviour in the underdoped regime (NMR and ARPES).Comment: 4 pages, RevTeX, 5 EPS figures included, to be published in Physical Review Letters vol 82, March 15, 199

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl

Dispersive Gap Mode of Phonons in Anisotropic Superconductors

We estimate the effect of the superconducting gap anisotropy in the dispersive gap mode of phonons, which is observed by the neutron scattering on borocarbide superconductors. We numerically analyze the phonon spectrum considering the electron-phonon coupling, and examine contributions coming from the gap suppression and the sign change of the pairing function on the Fermi surface. When the sign of the pairing function is changed by the nesting translation, the gap mode does not appear. We also discuss the suppression of the phonon softening of the Kohn anomaly due to the onset of superconductivity. We demonstrate that observation of the gap dispersive mode is useful for sorting out the underlying superconducting pairing function.Comment: 7 pages, 12 figures, to be published in J. Phys. Soc. Jp