15,486 research outputs found
Trace maps, invariants, and some of their applications
Trace maps of two-letter substitution rules are investigated with special
emphasis on the underlying algebraic structure and on the existence of
invariants. We illustrate the results with the generalized
Fibonacci chains and show that the well-known Fricke character
I(x,y,z) = x^2 + y^2 + z^2 - 2 x y z - 1 is not the only type of invariant
that can occur. We discuss several physical applications to electronic spectra
including the gap-labeling theorem, to kicked two-level systems, and to the
classical 1D Ising model with non-commuting transfer matrices.Comment: 23 pages, including 2 figures, paper made available here due to
renewed interes
Quantum corrections to broken N = 8 supergravity
We show that the one-loop effective potential of spontaneously broken N=8
supergravity is calculable and finite at all classical four-dimensional
Minkowski vacua without tachyons in the spectrum. The reason is that the
supertraces of the quadratic and quartic mass matrices vanish along the
classically flat directions: Str M^2 = Str M^4 =0. We also show that Str M^6 =
0 but Str M^8 > 0 in a broad class of vacua with broken supersymmetry on a flat
background, which includes all those explicitly identified so far. We find
analytical and numerical evidence that the corresponding one-loop effective
potential is negative-definite.Comment: 30 pages. v2: few misprints corrected. v3: JHEP published versio
Bases for qudits from a nonstandard approach to SU(2)
Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for
quantum information and quantum computation are constructed from angular
momentum theory and su(2) Lie algebraic methods. We report on a formula for
deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime
integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated
application of the formula can be used for generating mutually unbiased bases
in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection
between mutually unbiased bases and the unitary group SU(d) is briefly
discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on
Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in
memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of
Theoretical Physics of the JINR and the ICAS at Yerevan State University
SU(2) nonstandard bases: the case of mutually unbiased bases
This paper deals with bases in a finite-dimensional Hilbert space. Such a
space can be realized as a subspace of the representation space of SU(2)
corresponding to an irreducible representation of SU(2). The representation
theory of SU(2) is reconsidered via the use of two truncated deformed
oscillators. This leads to replace the familiar scheme {j^2, j_z} by a scheme
{j^2, v(ra)}, where the two-parameter operator v(ra) is defined in the
enveloping algebra of the Lie algebra su(2). The eigenvectors of the commuting
set of operators {j^2, v(ra)} are adapted to a tower of chains SO(3) > C(2j+1),
2j integer, where C(2j+1) is the cyclic group of order 2j+1. In the case where
2j+1 is prime, the corresponding eigenvectors generate a complete set of
mutually unbiased bases. Some useful relations on generalized quadratic Gauss
sums are exposed in three appendices.Comment: 33 pages; version2: rescaling of generalized Hadamard matrices,
acknowledgment and references added, misprints corrected; version 3:
published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA/ (22 pages
Effective Theory of Dark Energy at Redshift Survey Scales
We explore the phenomenological consequences of general late-time
modifications of gravity in the quasi-static approximation, in the case where
cold dark matter is non-minimally coupled to the gravitational sector. Assuming
spectroscopic and photometric surveys with configuration parameters similar to
those of the Euclid mission, we derive constraints on our effective description
from three observables: the galaxy power spectrum in redshift space,
tomographic weak-lensing shear power spectrum and the correlation spectrum
between the integrated Sachs-Wolfe effect and the galaxy distribution. In
particular, with CDM as fiducial model and a specific choice for the
time dependence of our effective functions, we perform a Fisher matrix analysis
and find that the unmarginalized CL errors on the parameters describing
the modifications of gravity are of order --. We
also consider two other fiducial models. A nonminimal coupling of CDM enhances
the effects of modified gravity and reduces the above statistical errors
accordingly. In all cases, we find that the parameters are highly degenerate,
which prevents the inversion of the Fisher matrices. Some of these degeneracies
can be broken by combining all three observational probes.Comment: 41 pages, 5 figures, 2 tables, improved analysis of ISW-galaxy
correlation, matches published version on JCA
On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
A class of pseudo-hermitian quantum system with an explicit form of the
positive-definite metric in the Hilbert space is presented. The general method
involves a realization of the basic canonical commutation relations defining
the quantum system in terms of operators those are hermitian with respect to a
pre-determined positive definite metric in the Hilbert space. Appropriate
combinations of these operators result in a large number of pseudo-hermitian
quantum systems admitting entirely real spectra and unitary time evolution. The
examples considered include simple harmonic oscillators with complex angular
frequencies, Stark(Zeeman) effect with complex electric(magnetic) field,
non-hermitian general quadratic form of N boson(fermion) operators, symmetric
and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian
Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of
Physics A(v3
Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions,
i.e., including a linear pseudoscalar potential and quadratic scalar and vector
potentials which have equal or opposite signs. We consider positive and
negative quadratic potentials and discuss in detail their bound-state solutions
for fermions and antifermions. The main features of these bound states are the
same as the ones of the generalized three-dimensional relativistic harmonic
oscillator bound states. The solutions found for zero pseudoscalar potential
are related to the spin and pseudospin symmetry of the Dirac equation in 3+1
dimensions. We show how the charge conjugation and chiral
transformations relate the several spectra obtained and find that for massless
particles the spin and pseudospin symmetry related problems have the same
spectrum, but different spinor solutions. Finally, we establish a relation of
the solutions found with single-particle states of nuclei described by
relativistic mean-field theories with scalar, vector and isoscalar tensor
interactions and discuss the conditions in which one may have both nucleon and
antinucleon bound states.Comment: 33 pages, 10 figures, uses revtex macro
- …