Geometric Phases for Mixed States during Cyclic Evolutions

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85}, 2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.Comment: 9 pages, 1 figur

Quantum confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density matrix renormalization group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation \delta) to study the ordering of the lowest one-photon (1^{1}B^{-}_u) and two-photon (2^{1}A^{+}_g) states in one- dimensional conjugated systems with chain lengths, N, up to N=80 sites. Three different types of crossovers are studied, as a function of U/t, \delta, and N. The U-crossover emphasizes the larger ionic character of the 2A_g state compared to the lowest triplet excitation. The \delta crossover shows strong dependence on both N and U/t. The N-crossover illustrates the more localized nature of the 2A_g excitation relative to the 1B_u excitation at intermediate correlation strengths.Comment: Latex file; figures available upon request. Submitted to PR

Bayesian Semiparametric Multivariate Density Deconvolution

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls

Current-voltage characteristics in donor-acceptor systems: Implications of a spatially varying electric field

We have studied the transport properties of a molecular device composed of donor and acceptor moieties between two electrodes on either side. The device is considered to be one-dimensional with different on-site energies and the non-equilibrium properties are calculated using Landauer's formalism. The current-voltage characteristics is found to be asymmetric with a sharp Negative Differential Resistance at a critical bias on one side and very small current on the other side. The NDR arises primarily due to the bias driven electronic structure change from one kind of insulating phase to another through a highly delocalized conducting phase. Our model can be considered to be the simplest to explain the experimental current-voltage characteristics observed in many molecular devices.Comment: 5 pages, 4 figures (accepted for publication in Physical Review B

Low-Lying Electronic Excitations and Nonlinear Optic Properties of Polymers via Symmetrized Density Matrix Renormalization Group Method

A symmetrized Density Matrix Renormalization Group procedure together with the correction vector approach is shown to be highly accurate for obtaining dynamic linear and third order polarizabilities of one-dimensional Hubbard and $U-V$ models. The $U-V$ model is seen to show characteristically different third harmonic generation response in the CDW and SDW phases. This can be rationalized from the excitation spectrum of the systems.Comment: 4 pages Latex; 3 eps figures available upon request; Proceedings of ICSM '96, to appear in Synth. Metals, 199

Continuous variable remote state preparation

We extend exact deterministic remote state preparation (RSP) with minimal classical communication to quantum systems of continuous variables. We show that, in principle, it is possible to remotely prepare states of an ensemble that is parameterized by infinitely many real numbers, i.e., by a real function, while the classical communication cost is one real number only. We demonstrate continuous variable RSP in three examples using (i) quadrature measurement and phase space displacement operations, (ii) measurement of the optical phase and unitaries shifting the same, and (iii) photon counting and photon number shift.Comment: 7 pages, RevTeX

Signatures of Nucleon Disappearance in Large Underground Detectors

For neutrons bound inside nuclei, baryon instability can manifest itself as a decay into undetectable particles (e.g., $\it n \to \nu \nu \bar{\nu}$), i.e., as a disappearance of a neutron from its nuclear state. If electric charge is conserved, a similar disappearance is impossible for a proton. The existing experimental lifetime limit for neutron disappearance is 4-7 orders of magnitude lower than the lifetime limits with detectable nucleon decay products in the final state [PDG2000]. In this paper we calculated the spectrum of nuclear de-excitations that would result from the disappearance of a neutron or two neutrons from $^{12}$C. We found that some de-excitation modes have signatures that are advantageous for detection in the modern high-mass, low-background, and low-threshold underground detectors, where neutron disappearance would result in a characteristic sequence of time- and space-correlated events. Thus, in the KamLAND detector [Kamland], a time-correlated triple coincidence of a prompt signal, a captured neutron, and a $\beta^{+}$ decay of the residual nucleus, all originating from the same point in the detector, will be a unique signal of neutron disappearance allowing searches for baryon instability with sensitivity 3-4 orders of magnitude beyond the present experimental limits.Comment: 13 pages including 6 figures, revised version, to be published in Phys.Rev.

General impossible operations in quantum information

We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We discuss why it is impossible to design a controlled-NOT gate for two unknown qubits and discuss the implications of these limitations.Comment: 15 pages, no figures, Discussion about personal quantum computer remove