On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

Capacities of noiseless quantum channels for massive indistinguishable particles: Bosons vs. fermions

We consider information transmission through a noiseless quantum channel, where the information is encoded into massive indistinguishable particles: bosons or fermions. We study the situation in which the particles are noninteracting. The encoding input states obey a set of physically motivated constraints on the mean values of the energy and particle number. In such a case, the determination of both classical and quantum capacity reduces to a constrained maximization of entropy. In the case of noninteracting bosons, signatures of Bose Einstein condensation can be observed in the behavior of the capacity. A major motivation for these considerations is to compare the information carrying capacities of channels that carry bosons with those that carry fermions. We show analytically that fermions generally provide higher channel capacity, i.e., they are better suited for transferring bits as well as qubits, in comparison to bosons. This holds for a large range of power law potentials, and for moderate to high temperatures. Numerical simulations seem to indicate that the result holds for all temperatures. Also, we consider the low temperature behavior for the three-dimensional box and harmonic trap, and again we show that the fermionic capacity is higher than the bosonic one for sufficiently low temperatures.Comment: 16 pages, 8 eps figures, RevTeX4; v2: small change in a figure; v3: significant new additions about quantum capacity, previous results unchanged, title changed, published versio

Implementation of generalized quantum measurements: superadditive quantum coding, accessible information extraction, and classical capacity limit

Quantum information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, the first experimental demonstration was reported [Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum coding gain, even in a small code length, can boost the communication performance of conventional coding technique.Comment: 15 pages, 14 figure

The enhancement of phase separation aspect in electron doped manganite Ca0.8Sm0.16Nd0.04MnO3

The complex lanthanide doping of electron manganites results in enhancement of various phase separation effects in physical properties of these compounds. Selecting Ca0.8Sm0.16Nd0.04MnO3 as a model case we show that the first order structural phase transition from paramagnetic semi-metallic phase into anti-ferromagnetic semi-metallic phase at TS ~ 158 +- 4 K is marked by an abrupt decrease in magnetization, a step like anomaly DL/L = 10-4 in thermal expansion and large latent heat DQ = 610 J/mol. In a certain temperature range below TS, the high field magnetization exhibits hysteretic metamagnetic behavior due to field-induced first order transformation. ac-susceptibility, magnetization and resistivity data suggest rather a non-uniform state in Ca0.8Sm0.16Nd0.04MnO3 at low temperatures. The metal - insulator transition occurs at TMI ~112 +- 3 K, accompanied by a step-like increase in magnetization. These features could be ascribed to "sponging" of electrons from neighboring anti-ferromagnetic matrix by clusters undergoing the ferromagnetic ordering.Comment: submitted to J.Phys. Cond. Matte

Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information

When an observer wants to identify a quantum state, which is known to be one of a given set of non-orthogonal states, the act of observation causes a disturbance to that state. We investigate the tradeoff between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable non-orthogonal pure states.Comment: 20 pages, standard LaTeX, four png figures (also available from the authors: [email protected] and [email protected]

Topological superfluid 3He-B in magnetic field and Ising variable

The topological superfluid 3He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of 3He-B. Magnetic field violates the time reversal symmetry. As a result, the topological invariant supported by this symmetry ceases to exist; and thus the gapless fermions on the surface of 3He-B are not protected any more by topology: they become fully gapped. Nevertheless, if perturbation of symmetry is small, the surface fermions remain relativistic with mass proportional to symmetry violating perturbation -- magnetic field. The 3He-B symmetry gives rise to the Ising variable I=+/- 1, which emerges in magnetic field and which characterizes the states of the surface of 3He-B. This variable also determines the sign of the mass term of surface fermions and the topological invariant describing their effective Hamiltonian. The line on the surface, which separates the surface domains with different I, contains 1+1 gapless fermions, which are protected by combined action of symmetry and topology.Comment: 5 pages, JETP Letters style, no figures, version submitted to JETP Letter

Magnetic properties of Ni2.18Mn0.82Ga Heusler alloys with a coupled magnetostructural transition

Polycrystalline Ni2.18Mn0.82Ga Heusler alloys with a coupled magnetostructural transition are studied by differential scanning calorimetry, magnetic and resistivity measurements. Coupling of the magnetic and structural subsystems results in unusual magnetic features of the alloy. These uncommon magnetic properties of Ni2.18Mn0.82Ga are attributed to the first-order structural transition from a tetragonal ferromagnetic to a cubic paramagnetic phase.Comment: 4 pages, 4 figures, revtex

Hawking Radiation and Unitary evolution

We find a family of exact solutions to the semi-classical equations (including back-reaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and transfers information faster than the theoretical bound for positive energy.Comment: LaTex file + uuencoded ps version including 4 figure

Music Perception Spring

The neuroanatomical correlates of temporal structure and expectancies in music were investigated using a unique stimulus manipulation involving scrambled music. The experiment compared brain responses (using functional magnetic resonance imaging) while participants listened to classical music and scrambled versions of that same music. The scrambled versions disrupted musical structure while holding low-level musical attributes constant, including such psychoacoustic parameters as pitch, loudness, and timbre. Comparing music to its scrambled counterpart, we found focal activation in the pars orbitalis region (Brodmann Area 47) of the left inferior frontal cortex, a region that has been previously closely associated with the processing of linguistic structure in spoken and signed language, and additional activation in the right hemisphere homologue of that area. We speculate that this particular region of inferior frontal cortex may be more generally responsible for processing fine-structured stimuli that evolve over time, not merely those that are linguistic