130 research outputs found
Double-Scaling Limit of the O(N)-Symmetric Anharmonic Oscillator
In an earlier paper it was argued that the conventional double-scaling limit
of an O(N)-symmetric quartic quantum field theory is inconsistent because the
critical coupling constant is negative and thus the integral representing the
partition function of the critical theory does not exist. In this earlier paper
it was shown that for an O(N)-symmetric quantum field theory in
zero-dimensional spacetime one can avoid this difficulty if one replaces the
original quartic theory by its PT-symmetric analog. In the current paper an
O(N)-symmetric quartic quantum field theory in one-dimensional spacetime [that
is, O(N)-symmetric quantum mechanics] is studied using the Schroedinger
equation. It is shown that the global PT-symmetric formulation of this
differential equation provides a consistent way to perform the double-scaling
limit of the O(N)-symmetric anharmonic oscillator. The physical nature of the
critical behavior is explained by studying the PT-symmetric quantum theory and
the corresponding and equivalent Hermitian quantum theory.Comment: ten pages, 4 figure
Nodal Liquids in Extended t-J Models and Dynamical Supersymmetry
In the context of extended t-J models, with intersite Coulomb interactions of
the form , with n_i denoting the electron
number operator at site i, nodal liquids are discussed. We use the spin-charge
separation ansatz as applied to the nodes of a d-wave superconducting gap.Such
a situation may be of relevance to the physics of high-temperature
superconductivity. We point out the possibility of existence of certain points
in the parameter space of the model characterized by dynamical supersymmetries
between the spinon and holon degrees of freedom, which are quite different from
the symmetries in conventional supersymmetric t-J models. Such symmetries
pertain to the continuum effective field theory of the nodal liquid, and one's
hope is that the ancestor lattice model may differ from the continuum theory
only by renormalization-group irrelevant operators in the infrared. We give
plausible arguments that nodal liquids at such supersymmetric points are
characterized by superconductivity of Kosterlitz-Thouless type. The fact that
quantum fluctuations around such points can be studied in a controlled way,
probably makes such systems of special importance for an eventual
non-perturbative understanding of the complex phase diagram of the associated
high-temperature superconducting materials.Comment: 39 pages latex, one eps, 2 latex figures incorporate
Comments on Extended t-J Models, Nodal Liquids and Supersymmetry
In the context of extended t-J models, with intersite Coulomb interactions,
nodal liquids are discussed. We use the spin-charge separation ansatz as
applied to the nodes of a d-wave superconducting gap. Such a situation may be
of relevance to the physics of high-temperature superconductivity. We point out
the possibility that at certain points of the parameter space supersymmetric
points may occur, characterized by dynamical supersymmetries between the spinon
and holon degrees of freedom, which are quite different from the symmetries in
conventional supersymmetric t-J models. Such symmetries pertain to the
continuum effective field theory of the nodal liquid, and one's hope is that
the ancestor lattice model may differ from the continuum theory only by
renormalization-group irrelevant operators in the infrared. We give plausible
arguments that nodal liquids at such supersymmetric points are characterized by
superconductivity of Kosterlitz-Thouless type.Comment: 18 pages latex, one eps figure incorporated (minor typos corrected).
Presented by N.E.M. at the Workshop ``Common Trends in Particle and Condensed
Matter Physics'', September 24-28 1999, Corfu (Greece
CPT-Violating Leptogenesis induced by Gravitational Defects
We explore leptogenesis induced by the propagation of neutrinos in
gravitational backgrounds that may occur in string theory. The first background
is due to linear dilatons and the associated Kalb-Ramond field (axion) in four
non-compact space-time dimensions of the string, and can be described within
the framework of local effective lagrangians. The axion is linear in the time
coordinate of the Einstein frame and gives rise to a constant torsion which
couples to the fermion spin through a gravitational covariant derivative. This
leads to different energy-momentum dispersion relations for fermions and
anti-fermions and hence leptogenesis. The next two backgrounds go beyond the
local effective lagrangian framework. One is a stochastic (Lorentz Violating)
Finsler metric which again leads to different dispersion relations between
fermions and antifermions. The third background of primary interest is the one
due to populations of stochastically fluctuating point-like space-time defects
that can be encountered in string/brane theory (D0 branes). Only neutral matter
interacts non-trivially with these defects, as a consequence of charge
conservation. Hence, such a background singles out neutrinos among the Standard
Model excitations as the ones interacting predominantly with the defects. The
back-reaction of the defects on the space-time due to their interaction with
neutral matter results in stochastic Finsler-like metrics (similar to our
second background). On average, the stochastic fluctuations of the D0 brane
defects preserve Lorentz symmetry, but their variance is non-zero.
Interestingly, the particle/antiparticle asymmetry comes out naturally to
favour matter over antimatter in this third background, once the effects of the
kinematics of the scattering of the D branes with matter is incorporated.Comment: 22 pages revtex 4-1, one eps figure incorporate
Fingerprints of Classical Instability in Open Quantum Dynamics
The dynamics near a hyperbolic point in phase space is modelled by an
inverted harmonic oscillator. We investigate the effect of the classical
instability on the open quantum dynamics of the oscillator, introduced through
the interaction with a thermal bath, using both the survival probability
function and the rate of von Neumann entropy increase, for large times. In this
parameter range we prove, using influence functional techniques, that the
survival probability function decreases exponentially at a rate, K', depending
not only on the measure of instability in the model but also on the strength of
interaction with the environment. We also show that K' determines the rate of
von Neumann entropy increase and that this result is independent of the
temperature of the environment. This generalises earlier results which are
valid in the limit of vanishing dissipation. The validity of inferring similar
rates of survival probability decrease and entropy increase for quantum chaotic
systems is also discussed.Comment: 13 pages, to be published in Physical Review
Spontaneous CPT Violation and Quantum Anomalies in a Model for Matter-Antimatter Asymmetry in the Cosmos
We review scenarios of baryogenesis through leptogenesis at early epochs of
the universe, in string-inspired minimal extensions of the Standard Model (SM),
involving heavy right-handed Majorana neutrinos. Spontaneous violation of CPT
symmetry is induced by appropriate (in general, temperature-dependent)
backgrounds of the Kalb-Ramond (KR) axion field, which has its origins in the
(bosonic) massless string multiplet. As interesting features of the model, we
also discuss two issues associated with quantum (chiral) anomalies: (i) the
non-contribution of the KR axion background to the (anomalous) chiral magnetic
effect, which arises in the presence of external electromagnetic fields and
non-zero chiral chemical potentials of charged fermions and (ii) the potential
r\^ole of quantum fluctuations of the KR axion on the (anomalous) radiative
generation of a Majorana mass for the right-handed neutrinos themselves.Comment: 18 pages rev tex. Plenary talk (by N.E.M.) at the 7th International
Conference of New Frontiers in Physics 2018, 4-12 July 2018, Kolymbari
(Greece); review with possible text overlap with: arXiv:1209.6387 [hep-ph],
arXiv:1403.7684 [hep-ph], arXiv:1412.7077 [hep-ph], arXiv:1712.03312
[hep-ph], arXiv:1810.13384 [hep-ph
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