701 research outputs found
On the Fock Transformation in Nonlinear Relativity
In this paper, we propose a new deformed Poisson brackets which leads to the
Fock coordinate transformation by using an analogous procedure as in Deformed
Special Relativity. We therefore derive the corresponding momentum
transformation which is revealed to be different from previous results.
Contrary to the earlier version of Fock's nonlinear relativity for which plane
waves cannot be described, our resulting algebra keeps invariant for any
coordinate and momentum transformations the four dimensional contraction
, allowing therefore to associate plane waves for free
particles. As in Deformed Special Relativity, we also derive a canonical
transformation with which the new coordinates and momentum satisfy the usual
Poisson brackets and therefore transform like the usual Lorentz vectors.
Finally, we establish the dispersion relation for Fock's nonlinear relativity.Comment: 10 pages, no figure
Unimodular cosmology and the weight of energy
Some models are presented in which the strength of the gravitational coupling
of the potential energy relative to the same coupling for the kinetic energy
is, in a precise sense, adjustable. The gauge symmetry of these models consists
of those coordinate changes with unit jacobian.Comment: LaTeX, 23 pages, conclusions expanded. Two paragraphs and a new
reference adde
The quantum dilogarithm and representations quantum cluster varieties
We construct, using the quantum dilogarithm, a series of *-representations of
quantized cluster varieties. This includes a construction of infinite
dimensional unitary projective representations of their discrete symmetry
groups - the cluster modular groups. The examples of the latter include the
classical mapping class groups of punctured surfaces.
One of applications is quantization of higher Teichmuller spaces.
The constructed unitary representations can be viewed as analogs of the Weil
representation. In both cases representations are given by integral operators.
Their kernels in our case are the quantum dilogarithms.
We introduce the symplectic/quantum double of cluster varieties and related
them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version.
To appear in Inventiones Math. The last Section of the previous versions was
removed, and will become a separate pape
Single-dot spectroscopy via elastic single-electron tunneling through a pair of coupled quantum dots
We study the electronic structure of a single self-assembled InAs quantum dot
by probing elastic single-electron tunneling through a single pair of weakly
coupled dots. In the region below pinch-off voltage, the non-linear threshold
voltage behavior provides electronic addition energies exactly as the linear,
Coulomb blockade oscillation does. By analyzing it, we identify the s and p
shell addition spectrum for up to six electrons in the single InAs dot, i.e.
one of the coupled dots. The evolution of shell addition spectrum with magnetic
field provides Fock-Darwin spectra of s and p shell.Comment: 7 pages, 3 figures, Accepted for publication in Phys. Rev. Let
Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
We report our rederivation of the equations of motion for relativistic
compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order
approximation to general relativity using the strong field point particle limit
to describe self-gravitating stars instead of the Dirac delta functional. The
computation is done in harmonic coordinates. Our equations of motion describe
the orbital motion of the binary consisting of spherically symmetric
non-rotating stars. The resulting equations of motion fully agree with the 3.5
PN equations of motion derived in the previous works. We also show that the
locally defined energy of the star has a simple relation with its mass up to
the 3.5 PN order.Comment: 38 pages, no figures. Accepted for publication in Phys. Rev.
Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order
The "dialogue of multipoles" matched asymptotic expansion for small black
holes in the presence of compact dimensions is extended to the Post-Newtonian
order for arbitrary dimensions. Divergences are identified and are regularized
through the matching constants, a method valid to all orders and known as
Hadamard's partie finie. It is closely related to "subtraction of
self-interaction" and shows similarities with the regularization of quantum
field theories. The black hole's mass and tension (and the "black hole
Archimedes effect") are obtained explicitly at this order, and a Newtonian
derivation for the leading term in the tension is demonstrated. Implications
for the phase diagram are analyzed, finding agreement with numerical results
and extrapolation shows hints for Sorkin's critical dimension - a dimension
where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio
Boundary Conditions on Internal Three-Body Wave Functions
For a three-body system, a quantum wave function with definite
and quantum numbers may be expressed in terms of an internal wave
function which is a function of three internal coordinates. This
article provides necessary and sufficient constraints on to
ensure that the external wave function is analytic. These
constraints effectively amount to boundary conditions on and its
derivatives at the boundary of the internal space. Such conditions find
similarities in the (planar) two-body problem where the wave function (to
lowest order) has the form at the origin. We expect the boundary
conditions to prove useful for constructing singularity free three-body basis
sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.
Angular Momentum Conservation Law for Randall-Sundrum Models
In Randall-Sundrum models, by the use of general Noether theorem, the
covariant angular momentum conservation law is obtained with the respect to the
local Lorentz transformations. The angular momentum current has also
superpotential and is therefore identically conserved. The space-like
components of the angular momentum for Randall-Sundrum models are
zero. But the component is infinite.Comment: 10 pages, no figures, accepted by Mod. Phys. Lett.
Gate Adjustable Coherent Three and Four Level Mixing in a Vertical Quantum Dot Molecule
We study level mixing in the single particle energy spectrum of one of the
constituent quantum dots in a vertical double quantum dot by performing
magneto-resonant-tunneling spectroscopy. The device used in this study differs
from previous vertical double quantum dot devices in that the single side gate
is now split into four separate gates. Because of the presence of natural
perturbations caused by anharmonicity and anistrophy, applying different
combinations of voltages to these gates allows us to alter the effective
potential landscape of the two dots and hence influence the level mixing. We
present here preliminary results from one three level crossing and one four
level crossings high up in the energy spectrum of one of the probed quantum
dots, and demonstrate that we are able to change significantly the energy
dispersions with magnetic field in the vicinity of the crossing regions.Comment: 5 pages, 4 figures. MSS-14 conference proceedings submitted to
Physica
Harmonic Initial-Boundary Evolution in General Relativity
Computational techniques which establish the stability of an
evolution-boundary algorithm for a model wave equation with shift are
incorporated into a well-posed version of the initial-boundary value problem
for gravitational theory in harmonic coordinates. The resulting algorithm is
implemented as a 3-dimensional numerical code which we demonstrate to provide
stable, convergent Cauchy evolution in gauge wave and shifted gauge wave
testbeds. Code performance is compared for Dirichlet, Neumann and Sommerfeld
boundary conditions and for boundary conditions which explicitly incorporate
constraint preservation. The results are used to assess strategies for
obtaining physically realistic boundary data by means of Cauchy-characteristic
matching.Comment: 31 pages, 14 figures, submitted to Physical Review
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