Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects

We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle, according to which the equations of motion of a point particle in such spaces can be obtained from the Newton equation in euclidean space by means of a nonholonomic mapping. By this principle, the known Langevin equation in euclidean space goes over into the correct Langevin equation in the Cartan space. This, in turn, serves to derive the Kubo and Fokker-Planck equations satisfied by the particle distribution as a function of time in such a space. The theory can be applied to classical diffusion processes in crystals with defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm

Autoparallels From a New Action Principle

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsionComment: Paper in src. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly with Netscape under http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm

Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor

The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct manifestation of inertia. The geometric origin of the torsion force is a closure failure of parallelograms. The torsion force changes the covariant conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm

Decrumpling membranes by quantum effects

The phase diagram of an incompressible fluid membrane subject to quantum and thermal fluctuations is calculated exactly in a large number of dimensions of configuration space. At zero temperature, a crumpling transition is found at a critical bending rigidity $1/\alpha_{\rm c}$. For membranes of fixed lateral size, a crumpling transition occurs at nonzero temperatures in an auxiliary mean field approximation. As the lateral size L of the membrane becomes large, the flat regime shrinks with $1/\ln L$.Comment: 9 pages, 4 figure

Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all n-point functions are derived by functional differentiation with respect to electron and photon propagators, and to the interaction. Basis for our construction is a functional differential equation obeyed by the vacuum energy when considered as a functional of the free propagators and the interaction. Our method does not employ external sources in contrast to traditional approaches.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/29

Coupled spin-charge drift-diffusion approach for a two-dimensional electron gas with Rashba spin-orbit coupling

Based on kinetic equations for the density matrix, drift-diffusion equations are derived for a two-dimensional electron gas with Rashba spin-orbit coupling. Universal results are obtained for the weak coupling case. Most interesting is the observation that with increasing spin-orbit coupling strengths there is a sharp transition between spin diffusion and ballistic spin transport. For strong spin-orbit coupling, when the elastic scattering time is much larger than the spin relaxation time, undamped spin-coherent waves are identified. The existence of these long-lived spin-coherent states is confirmed by exact analytical results obtained from microscopic kinetic equations valid in the ballistic regime.Comment: 16 pages, 3 figure

A General Expression for Symmetry Factors of Feynman Diagrams

The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory ($\phi^3$ and $\phi^4$ interactions), spinor QED, scalar QED, or QCD.Comment: RevTex 11 pages with 10 figure

Strings with Negative Stiffness and Hyperfine Structure

We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re27

Modulation and correlations lengths in systems with competing interactions

We examine correlation functions in the presence of competing long and short ranged interactions to find multiple correlation and modulation lengths. We calculate the ground state stripe width of an Ising ferromagnet, frustrated by an arbitrary long range interaction. In large $n$ systems, we demonstrate that for a short range system frustrated by a general competing long range interaction, the crossover temperature $T^*$ veers towards the critical temperature of the unfrustrated short range system (i.e., that in which the frustrating long range interaction is removed). We also show that apart from certain special crossover points, the total number of correlation and modulation lengths remains conserved. We derive an expression for the change in modulation length with temperature for a general system near the ground state with a ferromagnetic interaction and an opposing long range interaction. We illustrate that the correlation functions associated with the exact dipolar interactions differ substantially from those in which a scalar product form between the dipoles is assumed.Comment: 17 pages, 9 figure