Fluctuation, time-correlation function and geometric Phase

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast'' system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.Comment: Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Ge

Associated single photons and doubly charged scalar at linear e-e- colliders

Doubly charged scalars, predicted in many models having exotic Higgs representations, can in general have lepton-number violating (LFV) couplings. We show that by using an associated monoenergetic final state photon seen at a future linear e-e- collider, we can have a clear and distinct signature for a doubly-charged resonance. The strength of the Delta L=2 coupling can also be probed quite effectively as a function of the recoil mass of the doubly-charged scalar.Comment: Reference adde

Proton Decay and Related Processes in Unified Models with Gauged Baryon Number:

In unification models based on SU(15) or SU(16), baryon number is part of the gauge symmetry, broken spontaneously. In such models, we discuss various scenarios of important baryon number violating processes like proton decay and neutron-antineutron oscillation. Our analysis depends on the effective operator method, and covers many variations of symmetry breaking, including different intermediate groups and different Higgs boson content. We discuss processes mediated by gauge bosons and Higgs bosons parallely. We show how accidental global or discrete symmetries present in the full gauge invariant Lagrangian restrict baryon number violating processes in these models. In all cases, we find that baryon number violating interactions are sufficiently suppressed to allow grand unification at energies much lower than the usual $10^{16}$ GeV.Comment: (32 pages LATEX) [DOE-ER\,40757-022, CPP-93-22] {Small changes made and two references added. This version will appear in Phys. Rev. D

Non SUSY Unification in Left-Right Models

We explore in a model independent way the possibility of achieving the non supersymmetric gauge coupling unification within left-right symmetric models, with the minimal particle content at the left-right mass scale which could be as low as 1 TeV in a variety of models, and with a unification scale M in the range $10^5$ GeV $< M< 10^{17.7}$ GeV.Comment: 18 pages, Latex file, uses epsf style, four figures. Submitted for publication to Phys. Rev. D on Oct. 13, 199

Baryon and Lepton Number Assignment in E6E_6 Models

In $E_6$ models there are new particles whose baryon number is not uniquely assigned. We point out that the baryon and lepton number assignment to these particles can change the baryogenesis scenario significantly. We consider left-right symmetric extension of the standard model in which $(B-L)$ quantum number is gauged. The identification of $(B-L)$ with a generator of $E_6$ is used to define the baryon and lepton numbers for the exotic particles in a way that the electroweak baryon and lepton number anomaly corresponding to the $SU(2)_L$ group vanishes, {\it i.e.}, there is no non-perturbative baryon or lepton number violation during the electroweak phase transition. We study some consequences of the new assignment.Comment: 14 pages, LaTeX file, 1 submitted Figure file(.eps

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

Reply to "comment on Geometric phases for mixed states during cyclic evolutions"

We show that the geometric phase for mixed state during a cyclic evolution suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by nowaday techniques.Comment: Reply to the comment of Erik Sjoqvis

SU(16) grandunification: breaking scales, proton decay and neutrino magnetic moment

We give a detailed renormalization group analysis for the SU(16) grandunified group with general breaking chains in which quarks and leptons transform separately at intermediate energies. Our analysis includes the effects of Higgs bosons. We show that the grandunification scale could be as low as $\sim 10^{8.5}$ GeV and give examples where new physics could exist at relatively low energy ($\sim 250$ GeV). We consider proton decay in this model and show that it is consistent with a low grandunification scale. We also discuss the possible generation of a neutrino magnetic moment in the range of $10^{-11}$ to $10^{-10}\mu_B$ with a very small mass by the breaking of the embedded SU(2)$_\nu$ symmetry at a low energy.Comment: (16 pages in REVTEX + 6 figures not included) OITS-49

Superfluid-spiral state of quantum ferrimagnets in magnetic field

We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical non-linear $\sigma$ model of the quantum ferrimagnets at zero temperature and its effective description in the presence of the external magnetic field in terms of the quantum XY-model. The low- and the high-field phases correspond respectively to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field ($h_{c1} < h < h_{c2}$), it is an XXZ+h model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin-supercurrent. We derive the critical exponents, and then will study the stability of the XY spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at $h=h_{c2}$ if the spin-supercurrent reaches to its critical value.Comment: 6 pages and 4 figure

Probing SO(10) symmetry breaking patterns through sfermion mass relations

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of non-universal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these non-universal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these non-universal supersymmetry breaking scalar masses for the low energy phenomenology.Comment: 13 pages, latex using revtex4, contains 2 figures, replaced with version accepted for publicatio