7,143 research outputs found
Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature
We present a method utilizing the continuity equation for the condensate
density to make predictions of the precessional frequency of single off-axis
vortices and of vortex arrays in Bose-Einstein condensates at finite
temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB)
formalism. We solve the continuity equation for the condensate density
self-consistently with the orthogonalized HFB equations, and find stationary
solutions in the frame rotating at this frequency. As an example of the utility
of this formalism we obtain time-independent solutions for
quasi-two-dimensional rotating systems in the co-rotating frame. We compare
these results with time-dependent predictions where we simulate stirring of the
condensate.Comment: 13 pages, 11 figures, 1 tabl
Quantum Spin Lenses in Atomic Arrays
We propose and discuss `quantum spin lenses', where quantum states of
delocalized spin excitations in an atomic medium are `focused' in space in a
coherent quantum process down to (essentially) single atoms. These can be
employed to create controlled interactions in a quantum light-matter interface,
where photonic qubits stored in an atomic ensemble are mapped to a quantum
register represented by single atoms. We propose Hamiltonians for quantum spin
lenses as inhomogeneous spin models on lattices, which can be realized with
Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss
both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive
spin-spin interactions lead to focusing dynamics conditional to the number of
spin excitations. This allows the mapping of quantum superpositions of
delocalized spin excitations to superpositions of spatial spin patterns, which
can be addressed by light fields and manipulated. Finally, we propose
multifocal quantum spin lenses as a way to generate and distribute entanglement
between distant atoms in an atomic lattice array.Comment: 13 pages, 9 figure
Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout
Wigner crystals are prime candidates for the realization of regular electron
lattices under minimal requirements on external control and electronics.
However, several technical challenges have prevented their detailed
experimental investigation and applications to date. We propose an
implementation of two-dimensional electron lattices for quantum simulation of
Ising spin systems based on self-assembled Wigner crystals in transition-metal
dichalcogenides. We show that these semiconductors allow for minimally invasive
all-optical detection schemes of charge ordering and total spin. For incident
light with optimally chosen beam parameters and polarization, we predict a
strong dependence of the transmitted and reflected signals on the underlying
lattice periodicity, thus revealing the charge order inherent in Wigner
crystals. At the same time, the selection rules in transition-metal
dichalcogenides provide direct access to the spin degree of freedom via Faraday
rotation measurements.Comment: 15 pages, 12 figure
Discriminants, symmetrized graph monomials, and sums of squares
Motivated by the necessities of the invariant theory of binary forms J. J.
Sylvester constructed in 1878 for each graph with possible multiple edges but
without loops its symmetrized graph monomial which is a polynomial in the
vertex labels of the original graph. In the 20-th century this construction was
studied by several authors. We pose the question for which graphs this
polynomial is a non-negative resp. a sum of squares. This problem is motivated
by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the
derivative of a univariate polynomial, and an interesting example of P. and A.
Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative
but not a sum of squares. We present detailed information about symmetrized
graph monomials for graphs with four and six edges, obtained by computer
calculations
Defect mediated melting and the breaking of quantum double symmetries
In this paper, we apply the method of breaking quantum double symmetries to
some cases of defect mediated melting. The formalism allows for a systematic
classification of possible defect condensates and the subsequent confinement
and/or liberation of other degrees of freedom. We also show that the breaking
of a double symmetry may well involve a (partial) restoration of an original
symmetry. A detailed analysis of a number of simple but representative examples
is given, where we focus on systems with global internal and external (space)
symmetries. We start by rephrasing some of the well known cases involving an
Abelian defect condensate, such as the Kosterlitz-Thouless transition and
one-dimensional melting, in our language. Then we proceed to the non-Abelian
case of a hexagonal crystal, where the hexatic phase is realized if
translational defects condense in a particular rotationally invariant state.
Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference
PSY43 The Translation and Linguistic Validation of the Treatment Related Impact Measure – Weight (Trim-Weight)
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