3,413 research outputs found
Quantum Resonances and Ratchets in Free-Falling Frames
Quantum resonance (QR) is defined in the free-falling frame of the quantum
kicked particle subjected to gravity. The general QR conditions are derived.
They imply the rationality of the gravity parameter , the kicking-period
parameter , and the quasimomentum . Exact results are
obtained concerning wave-packet evolution for arbitrary periodic kicking
potentials in the case of integer (the main QRs). It is shown
that a quantum ratchet generally arises in this case for resonant . The
noninertial nature of the free-falling frame affects the ratchet by effectively
changing the kicking potential to one depending on . For a
simple class of initial wave packets, it is explicitly shown that the ratchet
characteristics are determined to a large extent by symmetry properties and by
number-theoretical features of .Comment: To appear in Physical Review E (Rapid Communications
Entanglement conditions and polynomial identities
We develop a rather general approach to entanglement characterization based
on convexity properties and polynomial identities. This approach is applied to
obtain simple and efficient entanglement conditions which work equally well in
both discrete as well as continuous-variable environments. Examples of
violations of our conditions are presented.Comment: 5 pages, no figure
q-Newton binomial: from Euler to Gauss
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made
less mysterious by virtue of being generalized through the introduction of an
additional parameter
Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case
In our previous paper \cite{co1} we have shown that the theory of circulant
matrices allows to recover the result that there exists Mutually Unbiased
Bases in dimension , being an arbitrary prime number. Two orthonormal
bases of are said mutually unbiased if
one has that ( hermitian scalar product in ). In this paper we show that the theory of block-circulant matrices with
circulant blocks allows to show very simply the known result that if
( a prime number, any integer) there exists mutually Unbiased
Bases in . Our result relies heavily on an idea of Klimov, Munoz,
Romero \cite{klimuro}. As a subproduct we recover properties of quadratic Weil
sums for , which generalizes the fact that in the prime case the
quadratic Gauss sums properties follow from our results
Phase operators, phase states and vector phase states for SU(3) and SU(2,1)
This paper focuses on phase operators, phase states and vector phase states
for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator
algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k <
0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and
infinite-dimensional representations of A(k,2) are constructed for k < 0 and k
> 0 or = 0, respectively. Phase operators associated with A(k,2) are defined
and temporally stable phase states (as well as vector phase states) are
constructed as eigenstates of these operators. Finally, we discuss a relation
between quantized phase states and a quadratic discrete Fourier transform and
show how to use these states for constructing mutually unbiased bases
Roots of the derivative of the Riemann zeta function and of characteristic polynomials
We investigate the horizontal distribution of zeros of the derivative of the
Riemann zeta function and compare this to the radial distribution of zeros of
the derivative of the characteristic polynomial of a random unitary matrix.
Both cases show a surprising bimodal distribution which has yet to be
explained. We show by example that the bimodality is a general phenomenon. For
the unitary matrix case we prove a conjecture of Mezzadri concerning the
leading order behavior, and we show that the same follows from the random
matrix conjectures for the zeros of the zeta function.Comment: 24 pages, 6 figure
Nilpotent Classical Mechanics
The formalism of nilpotent mechanics is introduced in the Lagrangian and
Hamiltonian form. Systems are described using nilpotent, commuting coordinates
. Necessary geometrical notions and elements of generalized differential
-calculus are introduced. The so called geometry, in a special case
when it is orthogonally related to a traceless symmetric form, shows some
resemblances to the symplectic geometry. As an example of an -system the
nilpotent oscillator is introduced and its supersymmetrization considered. It
is shown that the -symmetry known for the Graded Superfield Oscillator (GSO)
is present also here for the supersymmetric -system. The generalized
Poisson bracket for -variables satisfies modified Leibniz rule and
has nontrivial Jacobiator.Comment: 23 pages, no figures. Corrected version. 2 references adde
Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
We reformulate the Bekenstein bound as the requirement of positivity of the
Helmholtz free energy at the minimum value of the function L=E- S/(2\pi R),
where R is some measure of the size of the system. The minimum of L occurs at
the temperature T=1/(2\pi R). In the case of n-dimensional anti-de Sitter
spacetime, the rather poorly defined size R acquires a precise definition in
terms of the AdS radius l, with R=l/(n-2). We previously found that the
Bekenstein bound holds for all known black holes in AdS. However, in this paper
we show that the Bekenstein bound is not generally valid for free quantum
fields in AdS, even if one includes the Casimir energy. Some other aspects of
thermodynamics in anti-de Sitter spacetime are briefly touched upon.Comment: Latex, 32 page
On the sums of two cubes
We solve the equation for homogeneous , completing an investigation begun by Vi\`ete in 1591. The
usual addition law for elliptic curves and composition give rise to two binary
operations on the set of solutions. We show that a particular subset of the set
of solutions is ring-isomorphic to .Comment: Revised version, to appear in the International Journal of Number
Theor
- …