Geometry of effective Hamiltonians

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.Comment: 1 figur

Circular photon drag effect in bulk tellurium

The circular photon drag effect is observed in a bulk semiconductor. The photocurrent caused by a transfer of both translational and angular momenta of light to charge carriers is detected in tellurium in the mid-infrared frequency range. Dependencies of the photocurrent on the light polarization and on the incidence angle agree with the symmetry analysis of the circular photon drag effect. Microscopic models of the effect are developed for both intra- and inter-subband optical absorption in the valence band of tellurium. The shift contribution to the circular photon drag current is calculated. An observed decrease of the circular photon drag current with increase of the photon energy is explained by the theory for inter-subband optical transitions. Theoretical estimates of the circular photon drag current agree with the experimental data.Comment: 8 pages, 4 figure

Valley separation in graphene by polarized light

We show that the optical excitation of graphene with polarized light leads to the pure valley current where carriers in the valleys counterflow. The current in each valley originates from asymmetry of optical transitions and electron scattering by impurities owing to the warping of electron energy spectrum. The valley current has strong polarization dependence, its direction is opposite for normally incident beams of orthogonal linear polarizations. In undoped graphene on a substrate with high susceptibility, electron-electron scattering leads to an additional contribution to the valley current that can dominate.Comment: 4+ pages, 2 figure

Optimal purification of a generic n-qudit state

We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|\Psi>$ exactly equals the number of degrees of freedom of $\rho$, and (iii) $|\Psi>$ is easily determined from the density matrix $\rho$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.Comment: 8 pages, 9 figures, remarks adde

UCN Upscattering rates in a molecular deuterium crystal

A calculation of ultra-cold neutron (UCN) upscattering rates in molecular deuterium solids has been carried out, taking into account intra-molecular exictations and phonons. The different moelcular species ortho-D2 (with even rotational quantum number J) and para-D2 (with odd J) exhibit significantly different UCN-phonon annihilation cross-sections. Para- to ortho-D2 conversion, furthermore, couples UCN to an energy bath of excited rotational states without mediating phonons. This anomalous upscattering mechanism restricts the UCN lifetime to 4.6 msec in a normal-D2 solid with 33% para content.Comment: 3 pages, one figur

Conductance calculations for quantum wires and interfaces: mode matching and Green functions

Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green function techniques and an expression first derived by Caroli. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated originally by Ando, is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived and it is shown how all the Green function results can be derived from the mode matching technique. We illustrate this for a simple model which can be studied analytically, and for an Fe|vacuum|Fe tunnel junction which we study using first-principles calculations.Comment: 14 pages, 5 figure

Quantum Circulant Preconditioner for Linear System of Equations

We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1} A$, as well as the Frobenius norm $\|A\|_F$

Quantum communication and state transfer in spin chains

We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation

Morality of Labor and Labor Behavior

The article is devoted to concepts of morality, ethics which are some of the most common and at the same time some of the most multi-valued and uncertain ideas. Ethical problems appearing in some of the most important sides of human life are considered here