Search results for "values."
showing 10 items of 1353 documents
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.
Quantum search by parallel eigenvalue adiabatic passage
2008
We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap. The key to the efficiency is based on the use of parallel eigenvalues. This allows us to obtain non-adiabatic losses which are exponentially small, independently of the number of items in the database in which the search is performed.
Determination of the mobility edge in the Anderson model of localization in three dimensions by multifractal analysis.
1995
We study the Anderson model of localization in three dimensions with different probability distributions for the site energies. Using the Lanczos algorithm we calculate eigenvectors for different model parameters like disorder and energy. From these we derive the singularity spectrum typically used for the characterization of multifractal objects. We demonstrate that the singularity spectrum at the critical disorder, which determines the mobility edge at the band center, is independent of the employed probability distribution. Assuming that this singularity spectrum is universal for the metal-insulator transition regardless of specific parameters of the model we establish a straightforward …
High-precision atomic mass measurements for a CKM unitarity test
2013
Abstract The Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix describes the transformation of quarks from weak-force eigenstates to mass eigenstates. The most contributing element in this matrix is the up-down matrix element V ud , derived in most precise way from the nuclear beta decays and in particular, from decays having superallowed 0 + → 0 + decay branch. What high-precision mass spectrometry community can offer are decay energies of such decays derived from parent–daughter mass differences, which are ideally, and in almost all cases, determined with Penning trap mass spectrometry directly from parent–daughter cyclotron frequency ratio. Typically frequency (and thus mass) ratios a…
On Green's function for cylindrically symmetric fields of polarized radiation
2009
Analytic expressions for Green's function describing the process of transfer of polarized radiation in homogeneous isotropic infinite medium in case of cylindrical symmetry and nonconservative scattering are obtained. The solution is based on the set of systems of Abel integral equations of the first kind obtained using the principle of superposition, and the known expression of Green's function for radiation fields with plane-parallel symmetry. Eigenvalue decompositions for the corresponding matrices of generalized spherical functions are found. Using this result the systems of Abel integral equations are diagonalized, and the final solution is obtained.
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
2013
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schr\"odinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A…
Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry
2008
We describe a method for constructing vector coherent states for quantum supersymmetric partner Hamiltonians. The method is then applied to such partner Hamiltonians arising from a generalization of the fractional quantum Hall effect. Explicit examples are worked out.
Topological Hamiltonian as an exact tool for topological invariants
2012
We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show that topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
Pattern selection in the 2D FitzHugh–Nagumo model
2018
We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
Dynamics of a Quantum Particle in Asymmetric Bistable Potential with Environmental Noise
2011
In this work we analyze the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir. We obtain the time evolution of the population distributions in both energy and position eigenstates of the particle, for different values of the coupling strength with the thermal bath. The calculation is carried out using the Feynman-Vernon functional under the discrete variable representation.