39,262 research outputs found
New features of scattering from a one-dimensional non-Hermitian (complex) potential
For complex one-dimensional potentials, we propose the asymmetry of both
reflectivity and transmitivity under time-reversal: and , unless the potentials are real or PT-symmetric. For complex
PT-symmetric scattering potentials, we propose that
and . So far, the spectral singularities (SS) of a one-dimensional
non-Hermitian scattering potential are witnessed/conjectured to be at most one.
We present a new non-Hermitian parametrization of Scarf II potential to reveal
its four new features. Firstly, it displays the just acclaimed (in)variances.
Secondly, it can support two spectral singularities at two pre-assigned real
energies () either in or in , when
. Thirdly, when it possesses one SS in
and the other in . Fourthly, when the potential becomes PT-symmetric
, we get , it possesses a unique SS at
in both and . Lastly, for completeness, when
and , there are no SS, instead we get two
negative energies and of the complex PT-symmetric Scarf
II belonging to the two well-known branches of discrete bound state eigenvalues
and no spectral singularity exists in this case. We find them as
and ; with
.
{PACS: 03.65.Nk,11.30.Er,42.25.Bs}Comment: 10 pages, one Table, one Figure, important changes, appeared as an
FTC (J. Phys. A: Math. Theor. 45(2012) 032004
A method for predicting IGBT junction temperature under transient condition
In this paper, a method to predict junction temperature of the solid-state switch under transient condition is presented. The method is based on the thermal model of the switch and instantaneous measurement of the energy loss in the device. The method for deriving thermal model parameters from the manufacturers data sheet is derived and verified. A simulation work has been carried out on a single IGBT under different conditions using MATLAB/SIMULINK. The results show that the proposed method is effective to predict the junction temperature of the solid-state device during transient conditions and is applicable to other devices such as diodes and thyristors
Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
We extend the definition of generalized parity , charge-conjugation
and time-reversal operators to nondiagonalizable pseudo-Hermitian
Hamiltonians, and we use these generalized operators to describe the full set
of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold
classification. In particular we show that and are the generators of
the antiunitary symmetries; moreover, a necessary and sufficient condition is
provided for a pseudo-Hermitian Hamiltonian to admit a -reflecting
symmetry which generates the -pseudounitary and the -pseudoantiunitary
symmetries. Finally, a physical example is considered and some hints on the
-unitary evolution of a physical system are also given.Comment: 20 page
Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
We consider pseudo-unitary quantum systems and discuss various properties of
pseudo-unitary operators. In particular we prove a characterization theorem for
block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal
blocks. Furthermore, we show that every pseudo-unitary matrix is the
exponential of times a pseudo-Hermitian matrix, and determine the
structure of the Lie groups consisting of pseudo-unitary matrices. In
particular, we present a thorough treatment of pseudo-unitary
matrices and discuss an example of a quantum system with a
pseudo-unitary dynamical group. As other applications of our general results we
give a proof of the spectral theorem for symplectic transformations of
classical mechanics, demonstrate the coincidence of the symplectic group
with the real subgroup of a matrix group that is isomorphic to the
pseudo-unitary group U(n,n), and elaborate on an approach to second
quantization that makes use of the underlying pseudo-unitary dynamical groups.Comment: Revised and expanded version, includes an application to symplectic
transformations and groups, accepted for publication in J. Math. Phy
Shocks in unmagnetized plasma with a shear flow: Stability and magnetic field generation
A pair of curved shocks in a collisionless plasma is examined with a
two-dimensional particle-in-cell (PIC) simulation. The shocks are created by
the collision of two electron-ion clouds at a speed that exceeds everywhere the
threshold speed for shock formation. A variation of the collision speed along
the initially planar collision boundary, which is comparable to the ion
acoustic speed, yields a curvature of the shock that increases with time. The
spatially varying Mach number of the shocks results in a variation of the
downstream density in the direction along the shock boundary. This variation is
eventually equilibrated by the thermal diffusion of ions. The pair of shocks is
stable for tens of inverse ion plasma frequencies. The angle between the mean
flow velocity vector of the inflowing upstream plasma and the shock's
electrostatic field increases steadily during this time. The disalignment of
both vectors gives rise to a rotational electron flow, which yields the growth
of magnetic field patches that are coherent over tens of electron skin depths.Comment: 10 pages, 10 figures accepted for publication in Physics of Plasma
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