Spinorial matter and general relativity theory
Spinors in braided geometry
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
Splitting of the Dirac operator in the nonrelativistic limit
Splitting the conservation process into creation and annihilation parts
The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Spontaneously broken symmetries
Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group
Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
Stability and semiclassics in self-generated fields
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field.
Stability of matter in classical and quantized fields.
Stability of the Brown-Ravenhall operator.
Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems
This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the target in all homotopy classes and for the equivariant critical Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.
Staircase baker's map generates flaring-type time series.
Stark resonances for random potentials of Anderson type
State space properties of finite logics
Stationary Quantum Markov processes as solutions of stochastic differential equations
From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle, we can...
Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting
In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative...
Statistical maps. I: Basic properties
Statistical maps. II: Operational random variables and the Bell phenomenon
Statistics and quantum group symmetries
Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.