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

Neutrinoless double beta decay in SO(10) inspired seesaw models

By requiring the lower limit for the lightest right-handed neutrino mass, obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrino mass matrix similar to the up-quark mass matrix we predict small values for the $\nu_e$ mass and for the matrix element $m_{ee}$ responsible of the neutrinoless double beta decay, $m_{\nu_e}$ around $5\cdot10^{-3}$ eV and $m_{ee}$ smaller than $10^{-3}$ eV, respectively. The allowed range for the mass of the heaviest right-handed neutrino is centered around the value of the scale of B - L breaking in the SO(10) gauge theory with Pati-Salam intermediate symmetry.Comment: 9 pages, RevTex4. Revised, title change

Dark matter from SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on SU(4) and SU(2)xSU(2) groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the 4-th generation of fermions are the same as that of the ordinary-matter fermions in first three generations except for the family charge of the SU(4)_F group: F=(1/3,1/3,1/3,-1), where F=1/3 for fermions of ordinary matter and F=-1 for the 4-th generation. The difference in F does not allow the mixing between ordinary and fourth-generation fermions. Because of the conservation of the F charge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the 4-th generation. As a result the excess n_B of baryons over antibaryons leads to the excess n_{\nu 4}=N-\bar N=n_B of neutrinos over antineutrinos in the 4-th generation. This massive fourth-generation neutrino may form the non-baryonic dark matter. In principle their mass density n_{\nu 4}m_N in the Universe can give the main contribution to the dark matter, since the lower bound on neutrino mass m_N from the data on decay of the Z-bosons is m_N > m_Z/2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude bigger than allowed by observations. This inconsistency may be avoided by non-conservation of the F-charge.Comment: 9 pages, 2 figures, version accepted in JETP Letters, corrected after referee reports, references are adde

Alternating Spin and Orbital Dimerization in Strong-coupling Two-band Models

We study a one-dimensional Hamiltonian consisting of coupled SU(2) spin and orbital degrees of freedom. Using the density matrix renormalization group, we calculate the phase-diagram and the ground state correlation functions for this model. We find that, in addition to the ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The spin-gap and the order parameters are evaluated and the relevance to several recently discovered spin-gap materials is discussed.Comment: 4 pages REVTEX and 4 Postscript figure

Baryon and Lepton Number Violation with Scalar Bilinears

We consider all possible scalar bilinears, which couple to two fermions of the standard model. The various baryon and lepton number violating couplings allowed by these exotic scalars are studied. We then discuss which ones are constrained by limits on proton decay (to a lepton and a meson as well as to three leptons), neutron-antineutron oscillations, and neutrinoless double beta decay.Comment: 11 pages latex fil

Universal quantum Controlled-NOT gate

An investigation of an optimal universal unitary Controlled-NOT gate that performs a specific operation on two unknown states of qubits taken from a great circle of the Bloch sphere is presented. The deep analogy between the optimal universal C-NOT gate and the `equatorial' quantum cloning machine (QCM) is shown. In addition, possible applications of the universal C-NOT gate are briefly discussed.Comment: 18 reference

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.

"Assisted cloning'' and "orthogonal-complementing" of an unknown state

We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an unknown state with a minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation and in the second stage, the preparer disentangles the left-over entangled states by a single particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. We discuss our protocol for producing two copies and three copies (and complement copies) using two and four particle entangled state and suggest how to generalise this for N copies and complement copies using multiparticle entangled state.Comment: 7 pages, Latex, no figures, submitted to Phys. Rev. A. 1999(to be accepted

Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox

The black-hole information paradox has fueled a fascinating effort to reconcile the predictions of general relativity and those of quantum mechanics. Gravitational considerations teach us that black holes must trap everything that falls into them. Quantum mechanically the mass of a black hole leaks away as featureless (Hawking) radiation, but if the black hole vanishes, where is the information about the matter that made it? We treat the states of the in-fallen matter quantum mechanically and show that the black-hole information paradox becomes more severe. Our formulation of the paradox rules out one of the most conservative resolutions: that the state of the in-falling matter might be hidden in correlations between semi-classical Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semi-classical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.Comment: We first obtained this result two years ag

Two-dimensional Nanolithography Using Atom Interferometry

We propose a novel scheme for the lithography of arbitrary, two-dimensional nanostructures via matter-wave interference. The required quantum control is provided by a pi/2-pi-pi/2 atom interferometer with an integrated atom lens system. The lens system is developed such that it allows simultaneous control over atomic wave-packet spatial extent, trajectory, and phase signature. We demonstrate arbitrary pattern formations with two-dimensional 87Rb wavepackets through numerical simulations of the scheme in a practical parameter space. Prospects for experimental realizations of the lithography scheme are also discussed.Comment: 36 pages, 4 figure