Decoherence due to thermal effects in two quintessential quantum systems

Decoherence effects at finite temperature (T) are examined for two manifestly quantum systems: (i) Casimir forces between parallel plates that conduct along different directions, and (ii) a topological Aharonov-Bohm (AB) type force between fluxons in a superconductor. As we illustrate, standard path integral calculations suggest that thermal effects may remove the angular dependence of the Casimir force in case (i) with a decoherence time set by h/(k_{B} T) where h is Plank's constant and k_{B} is the Boltzmann constant. This prediction may be tested. The effect in case (ii) is due a phase shift picked by unpaired electrons upon encircling an odd number of fluxons. In principle, this effect may lead to small modifications in Abrikosov lattices. While the AB forces exist at extremely low temperatures, we find that thermal decoherence may strongly suppress the topological force at experimentally pertinent finite temperatures. It is suggested that both cases (i) and (ii) (as well as other examples briefly sketched) are related to a quantum version of the fluctuation-dissipation theorem.Comment: 15 pages, 2 figure

The BCS - BEC Crossover In Arbitrary Dimensions

Cold atom traps and certain neutron star layers may contain fermions with separation much larger than the range of pair-wise potentials yet much shorter than the scattering length. Such systems can display {\em universal} characteristics independent of the details of the short range interactions. In particular, the energy per particle is a fraction $\xi$ of the Fermi energy of the free Fermion system. Our main result is that for space dimensions D smaller than two and larger than four a specific extension of this problem readily yields $\xi=1$ for all $D \le 2$ whereas $\xi$ is rigorously non-positive (and potentially vanishing) for all $D \ge 4$. We discuss the D=3 case. A particular unjustified recipe suggests $\xi=1/2$ in D=3.Comment: 9 pages, 1 figur

Non-Relativistic Bose-Einstein Condensates, Kaon droplets, and Q- Balls

We note the similarity between BEC (Bose-Einstein Condensates) formed of atoms between which we have long-range attraction (and shorter-range repulsions) and the field theoretic "Q balls". This allows us in particular to address the stability of various putative particle physics Q balls made of non-relativistic bosons using variational methods of many-body physics

A Novel Approach to Complex Problems

A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g inside a graph G.Comment: 9 page

Characterizing Planar Graphs

Cataloging planar diagrams using the depth concept is proposed

Tests of CPT

The ongoing experimental efforts in the high energy and high precision communities keep providing evidence for CPT, a fundamental symmetry holding in any local Lorentz invariant theory. We suggest possible interconnections between different CPT violating parameters. Specifically, the very precise test of CPT in the $K^0-\bar K^0$ system suggests--though definitely does not imply--that CPT violations in other observable parameters (mass, width, charge, magnetic moments, etc.) are much smaller than the directly measured bounds.Comment: 7 pages, 1 figur

Exact Solutions to Special High Dimensional O(n) Models, Dimensional Reductions, gauge redundancy, and special Frustrated Spin and Orbital models

This work addresses models (e.g. potential models of directed orbital systems- the manganates) in which an effective reduction dimensionality occurs as a result of a new symmetry which is intermediate between that of global and local gauge symmetry. This path towards dimensional reduction is examined in simple O(n) spin models and lattice gauge theories. A high temperature expansion is employed to map special anisotropic high dimensional models into lower dimensional variants. We show that it is possible to have an effective reduction in the dimension without the need of compactifying some dimensions. These models are frustrated and display a symmetry intermediate between local and global gauge symmetries. Some solutions are presented. Our dimensional reductions are a generlization of the trivial dimensional reduction that occur in pure two dimensional gauge theories. It will be further seen that the absence of a ``phase interference'' effect plays an important role in high dimensional problems. By identifying another (``permutational'') symmetry present in the large n limit, we will further show how to generally map global high dimensional spin systems onto a one dimensional chain and discuss implications.Comment: 21 pages, 3 figure

Topological Charge Order and Binding in a Frustrated XY Model and Related systems

We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY models from a rather general vista. One of the complications that we face is the non-exact equivalence of the continuous (angular) XY model and its discrete topological charge dual. In reality, the energy spectra of the various topological sectors are highly nested much unlike that suggested by the discrete dual models. We surmount these difficulties by exploiting the Reflection Positivity symmetry that this periodic flux phase model possesses. The techniques introduced here may prove binding of topological charges in numerous models and might be applied to examine transitions associated with various topological defects, e.g., the confinement of disclinations in the isotropic to nematic transition.Comment: 16 pages, 3 figures, to appear in Journal of Statistical Mechanic

Viewpoint on the "Theory of the superglass phase" and a proof of principle of quantum critical jamming and related phases

A viewpoint article on the very interesting work of Biroli, Chamon, and Zamponi on superglasses. I further suggest how additional new superglass and "spin-superglass" phases of matter (the latter phases contain quenched disorder) and general characteristics may be proven as a theoretical proof of concept in various electronic systems. The new phases include: (1) superglasses of Cooper pairs, i.e., glassy superconductors, (2) superglass phases of quantum spins, and (3) superglasses of the electronic orbitals. New general features which may be derived by the same construct include (a) quantum dynamical heterogeneities- a low temperature quantum analogue of dynamical heterogeneities known to exist in classical glasses and spin-glasses wherein the local dynamics and temporal correlations are spatially non-uniform. I also discuss on a new class of quantum critical systems. In particular, I outline (b) the derivation of the quantum analogue of the zero temperature jamming transition that has a non-trivial dynamical exponent. We very briefly comment on (c) quantum liquid crystals.Comment: 3 pages sans figures and minor alterations of the published version; Physics 1, 40 (2008

From Higgs to pions and Back -- the Unbearable Lightness of a Composite Scalar Boson at 125 GeV in Purely Vectorial Theories

We argue that the $125 GeV$ "Higgs" particle is unlikely to arise as a fermion- antifermion composite if the underlying dynamics is a vectorial gauge theory. The reason is that the lightest scalar in such theories is heavier than the lightest pseudo-scalar with the mass difference being fixed by the scale of the theory. LHC searches suggest that the scale of any new physics, including that of a putative new theory dynamically generating the 125 GeV "Higgs" particle, is relatively high $\sim{(1/2TeV-1TeV)}$. Also the LHC analysis suggests that it is {\it scalar} namely $J^P = 0^+$ rather than pseudo-scalar. Thus it is unlikely that the "Higgs" could arise as a composite in such theories- though it will arise in special cases when the underlying binding gauge group is real as a fermion-fermion bound state. The direct considerations of the various two point functions in the large $N_c$ limit presented below- suggest that massless pseudo-scalars, but not any other anomalously light meson, arise as composites of massless fermions say the massless u and $\bar{d}$ quarks in QCD. These massless pions manifest the spontaneous breaking of the global axial symmetry in QCD with the pions being (pseudo) Nambu Goldstone Bosons. This offers a different insight into SXSB in QCD and most other confining non-abelian gauge vectorial gauge theory. Specifically we consider the euclidean two point functions $F_I|x-y|$ for asymptotic $|x-y|$ expressed as a sum over fermionic paths. We conjecture that for the pseudo-scalar two point function - and for that case only- self retracing paths and closely related paths make in this limit a positive, coherent and dominant contribution, a contribution which evades the generic asymptotic exponential fall-off and allows the lightest pseudoscalars to be massless. The same arguments imply that the scalars are very massive