Spin switching via quantum dot spin valves

We develop a theory for spin transport and magnetization dynamics in a quantum-dot spin valve, i.e., two magnetic reservoirs coupled to a quantum dot. Our theory is able to take into account effects of strong correlations. We demonstrate that, as a result of these strong correlations, the dot gate voltage enables control over the current-induced torques on the magnets, and, in particular, enables voltage-controlled magnetic switching. The electrical resistance of the structure can be used to read out the magnetic state. Our model may be realized by a number of experimental systems, including magnetic scanning-tunneling microscope tips and artificial quantum dot systems

All Hermitian Hamiltonians Have Parity

It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an eigenstate of P with eigenvalue (-1)^n. Given these properties, it is appropriate to refer to P as the parity operator and to say that H has parity symmetry, even though P may not refer to spatial reflection. Thus, if the Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses time-reversal symmetry), then it immediately follows that H has PT symmetry. This shows that PT symmetry is a generalization of Hermiticity: All Hermitian Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric Hamiltonians of this form are Hermitian

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval Δt\Delta t

The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval \Dt was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as $n!$. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is not excluded that for number of the potentials the expansion is convergent. For the polynomial potentials \Dt-expansion is certainly asymptotic one. The coefficients increase in this case as $\Gamma(n \frac{L-2}{L+2})$, where $L$ is the order of the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe

Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics

In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian $H={1\over2}p^2+{1\over2}x^2 +i\epsilon x^3$ using perturbative techniques. It is also shown how to construct the operator C for $H={1\over2}p^2+{1\over2}x^2-\epsilon x^4$ using nonperturbative methods

Lower bound of minimal time evolution in quantum mechanics

We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2\times 2 Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality of the polarization vector \bf P of the evolving quantum state \rho={1/2}(\bf 1+ \bf{P}\cdot\boldsymbol{\sigma}) with the vector \boldsymbol{\mathcal O}(\Theta) of the 2\times 2 hermitian Hamiltonians H ={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal O}(\Theta)\cdot\boldsymbol{\sigma}) and it is shown that the Hamiltonian H can be parameterized by two independent parameters {\mathcal O}_0 and \Theta.Comment: 4 pages, no figure, revtex

The stellar mass function of galaxies to z ~ 5 in the Fors Deep and GOODS-S fields

We present a measurement of the evolution of the stellar mass function (MF) of galaxies and the evolution of the total stellar mass density at 0<z<5. We use deep multicolor data in the Fors Deep Field (FDF; I-selected reaching I_AB=26.8) and the GOODS-S/CDFS region (K-selected reaching K_AB=25.4) to estimate stellar masses based on fits to composite stellar population models for 5557 and 3367 sources, respectively. The MF of objects from the GOODS-S sample is very similar to that of the FDF. Near-IR selected surveys hence detect the more massive objects of the same principal population as do I-selected surveys. We find that the most massive galaxies harbor the oldest stellar populations at all redshifts. At low z, our MF follows the local MF very well, extending the local MF down to 10^8 Msun. The faint end slope is consistent with the local value of alpha~1.1 at least up to z~1.5. Our MF also agrees very well with the MUNICS and K20 results at z<2. The MF seems to evolve in a regular way at least up to z~2 with the normalization decreasing by 50% to z=1 and by 70% to z=2. Objects having M>10^10 Msun which are the likely progenitors of todays L* galaxies are found in much smaller numbers above z=2. However, we note that massive galaxies with M>10^11 Msun are present even to the largest redshift we probe. Beyond z=2 the evolution of the mass function becomes more rapid. We find that the total stellar mass density at z=1 is 50% of the local value. At z=2, 25% of the local mass density is assembled, and at z=3 and z=5 we find that at least 15% and 5% of the mass in stars is in place, respectively. The number density of galaxies with M>10^11 Msun evolves very similarly to the evolution at lower masses. It decreases by 0.4 dex to z=1, by 0.6 dex to z=2, and by 1 dex to z=4.Comment: Accepted for publication in ApJ

Extended Jaynes-Cummings models and (quasi)-exact solvability

The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.Comment: 16 pages, 3 figures, discussion extended, one section adde

Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

We investigate the effects of competition between two complex, $\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and $V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$, represent long-range and localized gain/loss regions respectively. We obtain the $\mathcal{PT}$-symmetric phase in the $(Z,\xi)$ plane, and find that for locations $\pm a$ near the edge of the box, the $\mathcal{PT}$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $\mathcal{PT}$-symmetry will be restored by increasing the strength $\xi$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $\mathcal{PT}$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $\mathcal{PT}$-symmetric potentials show unique, unexpected properties.Comment: 7 pages, 3 figure

Searching for Massive Black Hole Binaries in the first Mock LISA Data Challenge

The Mock LISA Data Challenge is a worldwide effort to solve the LISA data analysis problem. We present here our results for the Massive Black Hole Binary (BBH) section of Round 1. Our results cover Challenge 1.2.1, where the coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence occurs after the simulated observational period. The data stream is composed of Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm is based on a variant of the Markov Chain Monte Carlo method that uses Metropolis-Hastings sampling and thermostated frequency annealing. We present results from the training data sets and the blind data sets. We demonstrate that our algorithm is able to rapidly locate the sources, accurately recover the source parameters, and provide error estimates for the recovered parameters.Comment: 11 pages, 6 figures, Submitted to CQG proceedings of GWDAW 11, AEI, Germany, Dec 200