3,515 research outputs found

### A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces

Dynamical systems associated with a q-deformed two dimensional phase space
are studied as effective dynamical systems described by ordinary variables. In
quantum theory, the momentum operator in such a deformed phase space becomes a
difference operator instead of the differential operator. Then, using the path
integral representation for such a dynamical system, we derive an effective
short-time action, which contains interaction terms even for a free particle
with q-deformed phase space. Analysis is also made on the eigenvalue problem
for a particle with q-deformed phase space confined in a compact space. Under
some boundary conditions of the compact space, there arises fairly different
structures from $q=1$ case in the energy spectrum of the particle and in the
corresponding eigenspace .Comment: 17page, 2 figure

### 5 Dimensional Spacetime with q-deformed Extra Space

An attempt to get a non-trivial-mass structure of particles in a
Randall-Sundrum type of 5-dimensional spacetime with q-deformed extra dimension
is discussed. In this spacetime, the fifth dimensional space is boundary free,
but there areises an elastic potential preventing free motion toward the fifth
direction. The q-deformation is, then, introduced in such a way that the
spacetime coordinates become non-commutative between 4-dimensional components
and the fifth component. As a result of this q-deformation, there arises
naturally an ultraviolet-cutoff effect for the propagators of particles
embedded in this spacetime.Comment: 14 pages, Latex file, 2 eps figure

### Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

The shift of the Bose-Einstein condensation temperature for a homogenous
weakly interacting Bose gas in leading order in the scattering length `a' is
computed for given particle density `n.' Variational perturbation theory is
used to resum the corresponding perturbative series for Delta/Nu in a
classical three-dimensional scalar field theory with coupling `u' and where the
physical case of N=2 field components is generalized to arbitrary N. Our
results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for
N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop
perturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications;
results unchange

### Investigation of the ion dose non-uniformity caused by sheath-lens focusing effect on silicon wafers

### $A$-cation control of magnetoelectric quadrupole order in $A$(TiO)Cu$_4$(PO$_4$)$_4$ ($A$ = Ba, Sr, and Pb)

Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric
activity is discovered in the novel compound $A$(TiO)Cu$_4$(PO$_4$)$_4$ with
$A$ = Pb, which is in contrast with antiferroic quadrupole order observed in
the isostructural compounds with $A$ = Ba and Sr. Unlike the famous lone-pair
stereochemical activity which often triggers ferroelectricity as in PbTiO$_3$,
the Pb$^{2+}$ cation in Pb(TiO)Cu$_4$(PO$_4$)$_4$ is stereochemically inactive
but dramatically alters specific magnetic interactions and consequently
switches the quadrupole order from antiferroic to ferroic. Our first-principles
calculations uncover a positive correlation between the degree of $A$-O bond
covalency and a stability of the ferroic quadrupole order.Comment: 7 pages, 4 figure

### Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and
relativistic systems with translational and rotational symmetry is derived in
the form of the commutator between the generator of dilations G and the
Hamiltonian H. If the conditions of translational and rotational symmetry
together with the additional conditions of the theorem are satisfied, the
matrix elements of the commutator [G, H] are equal to zero on the subspace of
the Hilbert space. Normalized simultaneous eigenvectors of the particular set
of commuting operators which contains H, J^{2}, J_{z} and additional operators
form an orthonormal basis in this subspace. It is expected that the theorem is
relevant for a large number of quantum mechanical N-particle systems with
translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of
Theoretical Physic

- â€¦