2,160,654 research outputs found
Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions
We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space
(X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime
with two times X^0,, X^0', unifies many physical systems which ordinarily are
described by a 1-time formulation. Different systems of 1-time physics emerge
by choosing gauges that embed ordinary time in d+2 dimensions in different
ways. The embeddings have different topology and geometry for the choice of
time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number
of 1-time physical interacting systems, and establishes a kind of duality among
them. One manifestation of the two times is that all of these physical systems
have the same quantum Hilbert space in the form of a unique representation of
SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning
degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of
the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical
systems that are unified in the same representation depend on n. The models we
study raise new questions about the nature of spacetime.Comment: Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is
modified; the more general potential is limited to a smaller clas
Quantum Abacus for counting and factorizing numbers
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and
Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The
algorithm makes use of qubits, qutrits, and qudits to count numbers in a base
2, base 3, or base d representation. In operating the algorithm, the number n <
N = d^K is read into a K-qudit register through its interaction with a stream
of n particles passing in a nearby wire; this step corresponds to a quantum
Fourier transformation from the Hilbert space of particles to the Hilbert space
of qudit states. An inverse quantum Fourier transformation provides the number
n in the base d representation; the inverse transformation is fully quantum at
the level of individual qudits, while a simpler semi-classical version can be
used on the level of qudit registers. Combining registers of qubits, qutrits,
and qudits, where d is a prime number, with a simpler single-shot measurement
allows to find the powers of 2, 3, and other primes d in the number n. We show,
that the counting task naturally leads to the shift operation and an algorithm
based on the quantum Fourier transformation. We discuss possible
implementations of the algorithm using quantum spin-d systems, d-well systems,
and their emulation with spin-1/2 or double-well systems. We establish the
analogy between our counting algorithm and the phase estimation algorithm and
make use of the latter's performance analysis in stabilizing our scheme.
Applications embrace a quantum metrological scheme to measure a voltage (analog
to digital converter) and a simple procedure to entangle multi-particle states.Comment: 23 pages, 15 figure
Universal Wave Function Overlap and Universal Topological Data from Generic Gapped Ground States
We propose a way -- universal wave function overlap -- to extract universal
topological data from generic ground states of gapped systems in any
dimensions. Those extracted topological data should fully characterize the
topological orders with gapped or gapless boundary. For non-chiral topological
orders in 2+1D, this universal topological data consist of two matrices,
and , which generate a projective representation of on the
degenerate ground state Hilbert space on a torus. For topological orders with
gapped boundary in higher dimensions, this data constitutes a projective
representation of the mapping class group of closed spatial manifold
. For a set of simple models and perturbations in two dimensions, we show
that these quantities are protected to all orders in perturbation theory
Localized Fermions on Domain Walls and Extended Supersymmetric Quantum Mechanics
We study fermionic fields localized on topologically unstable domain walls
bounded by strings in a grand unified theory theoretical framework.
Particularly, we found that the localized fermionic degrees of freedom, which
are up and down quarks as long as charged leptons, are connected to three
independent N=2, supersymmetric quantum mechanics algebras. As we
demonstrate, these algebras can be combined to form higher order
representations of N=2, supersymmetry. Due to the uniform coupling of the
domain wall solutions to the down-quarks and leptons, we also show that a
higher order N=2, representation of the down-quark--lepton system is
invariant under a duality transformation between the couplings. In addition,
the two N=2, supersymmetries of the down-quark--lepton system, combine at
the coupling unification scale to an N=4, supersymmetry. Furthermore, we
present the various extra geometric and algebraic attributes that the fermionic
systems acquire, owing to the underlying N=2, algebras.Comment: Revised versio
Particle-hole condensates of higher angular momentum in hexagonal systems
Hexagonal lattice systems (e.g. triangular, honeycomb, kagome) possess a
multidimensional irreducible representation corresponding to and
symmetry. Consequently, various unconventional phases that combine
these -wave representations can occur, and in so doing may break
time-reversal and spin rotation symmetries. We show that hexagonal lattice
systems with extended repulsive interactions can exhibit instabilities in the
particle-hole channel to phases with either or
symmetry. When lattice translational symmetry is preserved, the phase
corresponds to nematic order in the spin-channel with broken time-reversal
symmetry, known as the phase. On the other hand, lattice translation
symmetry can be broken, resulting in various density wave
orders. In the weak-coupling limit, when the Fermi surface lies close to a van
Hove singularity, instabilities of both types are obtained in a controlled
fashion.Comment: 6 pages, 3 figures. Journal reference adde
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