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Hagen Kleinert

Publications and source records attributed to Hagen Kleinert.

At least 37 records · Page 2Linked to original sources
arXiv2011

Disorder effects at a nematic quantum critical point in d-wave cuprate superconductor

A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effect on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization group analysis shows that random mass and random gauge field are both irrelevant and thus do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.

cond-mat.str-el↗
arXiv2011

High Bias Voltage Transport in Metallic Single-walled Carbon Nanotubes under Axial Stress

We calculate the current-voltage characteristic of a homogeneously strained metallic carbon nanotube adsorbed on a substrate. The strain generates a gap in the energy spectrum leading to a reduction of the current. In the elastic regime, the current-voltage characteristic shows a large negative differential conductance at bias voltages of around $ \gtrsim 0.17 $V. We discuss the implications for the current in the superelongated regime.

cond-mat.mes-hall↗
arXiv2011

Quantum Maupertuis Principle

According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{μν}(x)=2M[V(x)-E]δ_{μν}$. We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schrödinger equation in curved space where the kinetic operator is formed with the {\it Weyl--invariant Laplace-Beltrami} operator. As an application, we use DeWitt's recursive semiclassical expansion of the time-evolution operator in curved space to calculate the semiclassical expansion of the particle density $ρ(x;E)= $.

quant-ph↗
arXiv2010

Optical Phonon Lineshapes and Transport in Metallic Carbon Nanotubes under High Bias Voltage

We calculate the current-voltage characteristic of metallic nanotubes at high bias voltage showing that a bottleneck exists for short nanotubes in contrast to large ones. We attribute this to a redistribution of lower-lying acoustic phonons caused by phonon-phonon scattering with hot optical phonons. The current-voltage characteristic and the electron and phonon distribution functions are derived analytically, and serve to obtain in a self-contained way the frequency shift and line broadening of the zone center optical phonons due to the electron-phonon coupling at high bias. We obtain a positive frequency shift from the zero bias shift and no broadening of the optical phonon mode at very high voltages, in agreement with recent experiments.

cond-mat.mes-hall↗
arXiv2010

Superstatistics approach to path integral for a relativistic particle

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schroedinger-Dirac representation. As a byproduct we recover the worldline representation of Klein-Gordon and Dirac propagators, and discuss the role of the smearing distributions in fixing the reparametrization freedom. The emergent relativity picture that follows from our approach together with a novel representation of the Lorentz group for the Feshbach-Villars particle are also discussed.

hep-th↗
arXiv2009

Uncertainty Relation on World Crystal and its Applications to Micro Black Holes

We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of the order of Planck length -- "world crystal". In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. We also briefly mention some connections of the world crystal paradigm with 't Hooft's quantization and double special relativity.

hep-th↗
arXiv2008

Photoproduction in semiconductors by onset of magnetic field

The energy bands of a semiconductor are lowered by an external magnetic field. When a field is switched on, the straight-line trajectories near the top of the occupied valence band are curved into Landau orbits and Bremsstrahlung is emitted until the electrons have settled in their final Fermi distribution. We calculate the radiated energy, which should be experimentally detectable, and suggest that a semiconductor can be cooled by an oscillating magnetic field.

cond-mat.other↗
arXiv2008

Superpositions of Probability Distributions

Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v = σ^2 play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in v which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics.

cond-mat.other↗
arXiv2008

Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields

Treating the production of electron and positron pairs by a strong electric field from the vacuum as a quantum tunneling process we derive, in semiclassical approximation, a general expression for the pair production rate in a $z$-dependent electric field $E(z)$ pointing in the $z$-direction. We also allow for a smoothly varying magnetic field parallel to $E(z)$. The result is applied to a confined field $E(z)\not=0$ for $|z|\lesssim \ell $, a semi-confined field $E(z)\not=0$ for $ z\gtrsim 0 $, and a linearly increasing field $E(z)\sim z$. The boundary effects of the confined fields on pair-production rates are exhibited. A simple variable change in all formulas leads to results for electric fields depending on time rather than space. In addition, we discuss tunneling processes in which empty atomic bound states are spontaneously filled by negative-energy electrons from the vacuum under positron emission. In particular, we calculate the rate at which the atomic levels of a bare nucleus of finite size $r_{\rm n}$ and large $Z\gg 1$ are filled by spontaneous pair creation.

hep-th↗
arXiv2007

Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.

cond-mat.stat-mech↗
arXiv2007

Smearing Distributions and their use in Financial Markets

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing "smearing" distributions substantially simplify the coupled system of Fokker-Planck equations for smeared and un-smeared conditional probabilities. Simple application in financial models with stochastic volatility is presented.

q-fin.ST↗
arXiv2007

Perturbation Expansion for Option Pricing with Stochastic Volatility

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black-Scholes expressions. An explicit analytic formula is deduced from a perturbation expansion around a Black-Scholes formula with the mean volatility. The expansion has two parts. The first takes into account the non-Gaussian character of the stock-fluctuations and is organized by powers of the excess kurtosis, the second is contract based, and is organized by the moments of moneyness of the option. With this expansion we show that for the Dow Jones Euro Stoxx 50 option data, a Delta-hedging strategy is close to being optimal.

q-fin.PR↗
arXiv2007

Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis

We discuss compact (2+1)-dimensional Maxwell electrodynamics coupled to fermionic matter with N replica. For large enough N, the latter corresponds to an effective theory for the nearest neighbor SU(N) Heisenberg antiferromagnet, in which the fermions represent solitonic excitations known as spinons. Here we show that the spinons are deconfined for $N>N_c=36$, thus leading to an insulating state known as spin liquid. A previous analysis considerably underestimated the value of $N_c$. We show further that for $20<N\leq 36$ there can be either a confined or a deconfined phase, depending on the instanton density. For $N\leq 20$ only the confined phase exist. For the physically relevant value N=2 we argue that no paramagnetic phase can emerge, since chiral symmetry breaking would disrupt it. In such a case a spin liquid or any other nontrivial paramagnetic state (for instance, a valence-bond solid) is only possible if doping or frustrating interactions are included.

cond-mat.str-el↗
arXiv2007

Critical Temperature of Weakly Interacting Dipolar Condensates

We calculate perturbatively the effect of a dipolar interaction upon the Bose-Einstein condensation temperature. This dipolar shift depends on the angle between the symmetry axes of the trap and the aligned atomic dipole moments, and is extremal for parallel or orthogonal orientations, respectively. The difference of both critical temperatures exhibits most clearly the dipole-dipole interaction and can be enhanced by increasing both the number of atoms and the anisotropy of the trap. Applying our results to chromium atoms, which have a large magnetic dipole moment, shows that this dipolar shift of the critical temperature could be measured in the ongoing Stuttgart experiment.

cond-mat.stat-mech↗
arXiv2006

Thermally induced rotons in two-dimensional dilute Bose gases

We show that roton-like excitations are thermally induced in a two-dimensional dilute Bose gas as a consequence of the strong phase fluctuations in two dimensions. At low momentum, the roton-like excitations lead for small enough temperatures to an anomalous phonon spectrum with a temperature dependent exponent reminiscent of the Kosterlitz-Thouless transition. Despite the anomalous form of the energy spectrum, it is shown that the corresponding effective theory of vortices describes the usual Kosterlitz-Thouless transition. The possible existence of an anomalous normal state in a small temperature interval is also discussed.

cond-mat.other↗
arXiv2005

Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids

Compact quantum electrodynamics in 2+1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when $N>N_c=36/π^3\approx 1.161$, where $N$ is the number of fermion replica. For $N<N_c$, however, there are two stable fixed points separated by a line containing a unstable non-trivial fixed point: a fixed point corresponding to the scaling limit of the non-compact theory, and another one governing the scaling behavior of the compact theory. The string tension associated to the confining interspinon potential is shown to exhibit a universal jump as $N\to N_c^-$. Our results imply the stability of a spin liquid at the physical value N=2 for Mott insulators.

cond-mat.str-el↗
arXiv2005

Path Integral Approach to 't Hooft's Derivation of Quantum from Classical Physics

We present a path-integral formulation of 't Hooft's derivation of quantum from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.

quant-ph↗