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: $R(-k)\ne R(k)$ and $T(-k) \ne T(k)$, unless the potentials are real or PT-symmetric. For complex PT-symmetric scattering potentials, we propose that $R_{left}(-k)=R_{right}(k)$ and $T(-k)=T(k)$. 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 ($E_*=\alpha^2,\beta^2$) either in $T(k)$ or in $T(-k)$, when $\alpha\beta>0$. Thirdly, when $\alpha \beta <0$ it possesses one SS in $T(k)$ and the other in $T(-k)$. Fourthly, when the potential becomes PT-symmetric $[(\alpha+\beta)=0]$, we get $T(k)=T(-k)$, it possesses a unique SS at $E=\alpha^2$ in both $T(-k)$ and $T(k)$. Lastly, for completeness, when $\alpha=i\gamma$ and $\beta=i\delta$, there are no SS, instead we get two negative energies $-\gamma^2$ and $-\delta^2$ 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 $E^{+}_{M}=-(\gamma-M)^2$ and $E^{-}_{N}=-(\delta-N)^2$; $M(N)=0,1,2,...$ with $0 \le M (N)< \gamma (\delta)$. {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 $P$, charge-conjugation $C$ and time-reversal $T$ 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 $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-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 $i=\sqrt{-1}$ 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 $2\times 2$ pseudo-unitary matrices and discuss an example of a quantum system with a $2\times 2$ 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 $Sp(2n)$ 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