Symplectic, orthogonal and linear Lie groups in Clifford algebra
September 8, 2014
|
Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
In this paper we prove isomorphisms between 5 Lie groups (of arbitrary
dimension and fixed signatures) in Clifford algebra and classical matrix Lie
groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms
of correspond...
Normal Forms and Degenerate CR Singularities
August 28, 2014
Mathematics
Complex Variables
Differential Geometry
It is constructed a normal form for a class of real-smooth surfaces
M\subset\mathbb{C}^{2} defined near a degenerate CR singularity....
Matrix integrals over unitary groups: An application of Schur-Weyl
duality
August 16, 2014
Physics
Mathematics
Quantum Physics
Mathematical Physics
Mathematical Physics
The integral formulae pertaining to the unitary group U(d) have
been comprehensively reviewed, yielding fresh results and innovative proofs.
Central to the derivation of these formulae lies the employment of Schur-Weyl
duality, a...
Self-assembled porous media from particle-stabilized emulsions
August 13, 2014
|
Physics
Soft Condensed Matter
Materials Science
Chemical Physics
Computational Physics
Fluid Dynamics
We propose a new mechanism to create self-assembled porous media with highly
tunable geometrical properties and permeabilities: We first allow a
particle-stabilized emulsion to form from a mixture of two fluids and colloidal
particles. Then...
Infinite-dimensional stochastic differential equations arising from Airy
random point fields
August 4, 2014
|
Mathematics
Physics
Probability
Mathematical Physics
Mathematical Physics
The Airyβ random point fields (β=1,2,4) are random point
fields emerging as the soft-edge scaling limits of eigenvalues of Gaussian
random matrices. We construct the unlabeled diffusion reversible with respect
to the Airy...
Roles of Hund's rule coupling in excitonic density-wave states
July 17, 2014
|
Physics
Strongly Correlated Electrons
Excitonic density-wave states realized by the quantum condensation of
electron-hole pairs (or excitons) are studied in the two-band Hubbard model
with Hund's rule coupling and the pair hopping term. Using the variational
cluster approximati...
In Quantum Computing Speedup Illusory?: The False Coin of "Counting
Function Evaluations"
July 16, 2014
Physics
Quantum Physics
By using a new way to encode Boolean functions in a reversible gate, an
algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as
opposed to QC over C) that needs only one function evaluation to solve the
Grover Database Se...
A theory for the zeros of Riemann ζ and other L-functions
(updated)
July 16, 2014
|
Mathematics
Physics
Number Theory
High Energy Physics - Theory
Mathematical Physics
Mathematical Physics
In these lectures we first review the important properties of the Riemann
ζ-function that are necessary to understand the nature and importance of
the Riemann hypothesis (RH). In particular this first part describes the
analytic conti...
Synchrotron radiation of vector bosons at relativistic colliders
July 9, 2014
Physics
High Energy Physics - Phenomenology
Magnetic fields produced in collisions of electrically charged particles at
relativistic energies are strong enough to affect the dynamics of the strong
interactions. In particular, it induces radiation of vector bosons by
relativistic ferm...
The missing proof of Paley's theorem about lacunary coefficients
July 6, 2014
Mathematics
Classical Analysis and ODEs
We modify the standard proof of Paley's theorem about lacunary coefficients
of functions in H1 to work without analytic factorization. This leads to the
first direct proof of the extension of Paley's theorem that we applied to the
former...