Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach

Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [14,18] for the particular case N = 1 and N = 2 respectively.Comment: Some references have been adde

Entanglement of subspaces in terms of entanglement of superpositions

We investigate upper and lower bounds on the entropy of entanglement of a superposition of bipartite states as a function of the individual states in the superposition. In particular, we extend the results in [G. Gour, arxiv.org:0704.1521 (2007)] to superpositions of several states rather than just two. We then investigate the entanglement in a subspace as a function of its basis states: we find upper bounds for the largest entanglement in a subspace and demonstrate that no such lower bound for the smallest entanglement exists. Finally, we consider entanglement of superpositions using measures of entanglement other than the entropy of entanglement.Comment: 7 pages, no figure

Phase properties of a new nonlinear coherent state

We study phase properties of a displacement operator type nonlinear coherent state. In particular we evaluate the Pegg-Barnett phase distribution and compare it with phase distributions associated with the Husimi Q function and the Wigner function. We also study number- phase squeezing of this state.Comment: 8 eps figures. to appear in J.Opt

Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or

Interesting thermomagnetic history effects in the antiferromagnetic state of SmMn_2Ge_2

We present results of magnetization measurements showing that the magnetic response of the antiferromagnetic state of SmMn_2Ge_2 depends on the path used in the field(H)-temperature(T) phase space to reach this state. Distinct signature of metastablity is observed in this antiferromagnetic state when obtained via field-cooling/field-warming paths. The isothermal M-H loops show lack of end-point memory, reminiscent of that seen in metastable vortex states near the field-induced first order phase transition in various type-II superconductors.Comment: 11 pages of text and 3 figure

Electron transport in sub-micron GaAs channels at 300 K

Transient velocity-field characteristics have been computed for GaAs channels having lengths of 0.1, 0.2, 0.5, 1, and 20 µm for electric fields between 1 and 50 kV/cm at 300 K. The results are compared with earlier calculations and the significant features of the computed results are discussed. It is found that the electron motion for all channel lengths and for all fields is significantly affected by collisions. The threshold field for negative differential mobility increases, and the magnitude of the differential mobility decreases with decrease in the length of the sample. The maximum steady-state velocity increases with decrease in the length and may be as high as 5.4×107 cm/s for 0.1 µm samples