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Alexander Jurisch

Publications and source records attributed to Alexander Jurisch.

11 recordsLinked to original sources
arXiv2020

On Newton's equation of motion with friction and stochastic noise, the Ostrogradsky-instability and the hierarchy of environments, An application of the Onsager-Machlup theory II

Onsager and Machlup proposed a second order variational-principle in order to include inertial effects into the Langevin-equation, giving a Lagrangian with second order derivatives in time. This but violates Ostrogradysky's theorem, which proves that Lagrangians with higher than first order derivatives are meaningless. As a consequence, inertial effects cannot be included in a standard way. By using the canonical formalism, we suggest a solution to this fundamental problem. Furthermore, we provide elementary arguments about the hierarchy of immersions and actions between an ideal system and several environments and show, that the structure of the Lagrangian sensitively depends on this hierarchy.

cond-mat.stat-mech↗
arXiv2020

Lagrangian dynamics in inhomogeneous and thermal environments, An application of the Onsager-Machlup theory I

We straight-forwardly derive the Onsager-Machlup Lagrangian from the Fokker-Planck equation and show that friction and dissipation are a natural property of the equation of motion. We develop a method to calculate the local variance $σ_{2}\,b(q)^{2}$ and identify this function as a Helmholtz-factor. In both meanings the function $b(q)$ describes properties of the environment. For application, we examine the free fall through a barometric medium and model a blow of wind by a solitonic pulse running through the medium. We treat harmonic oscillators immersed in a thermal bath, finding intuitive as well as counter-intuitive phenomena of friction. By allowing the temperature to be time-dependent, the dynamical process of cooling and heating becomes self-consistently available. We find a state of dynamical balance between system and environment. Last, we show that dynamical balance is related to adiabatic thermodynamic processes. In a special case, dynamical balance can induce a real phase-transition.

cond-mat.stat-mech↗
arXiv2020

Brownian motion approach to anomalous rotation of galaxies

It has been shown that the weak-interacting limit of the metric-skew-tensor-gravity (MSTG) can explain the anomalous rotation of galaxies without non-baryonic dark matter. We show that MSTG is related to the equilibrium-state of ordinary Brownian motion. We also explore if other stochastic processes can model anomalous rotation. Furthermore, we analyze phase-diagrams that elucidate the condensation of a gravitating cloud towards a Kepler-Newton system and illustrate regions of existence of rotating objects.

cond-mat.stat-mech↗
arXiv2019

Statistical mechanics and time-series analysis by Lévy-parameters with the possibility of real-time application

We develop a method that relates the truncated cumulant-function of the fourth order with the Lévian cumulant-function. This gives us explicit formulas for the Lévy-parameters, which allow a real-time analysis of the state of a random-motion. Cumbersome procedures like maximum-likelihood or least-square methods are unnecessary. Furthermore, we treat the Lévy-system in terms of statistical mechanics and work out it's thermodynamic properties. This also includes a discussion of the fractal nature of relativistic corrections. As examples for a time-series analysis, we apply our results on the time-series of the German DAX and the American S\&P-500\,.

cond-mat.stat-mech↗
arXiv2019

An extremal fractional Gaussian with a possible application to option-pricing with skew and smile

We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry out an analysis of the structure of the implied volatility in this system.

q-fin.PR↗
arXiv2019

Calculation of eigenvalues by Greens-functions and the Lippmann-Schwinger equation

We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and quartic oscillator, a symmetric and a skew double-well potential, and potentials with finite and infinite depth. Furthermore, we show how our method can be used for eigenvalue-engineering.

quant-ph↗
arXiv2009

Anomalous quantum reflection as a quasi-dynamical damping effect

We develop a quasi-analytical theory for the quantum reflection amplitude of Bose-Einstein condensates. We derive and calculate the decay-width of a Bose-Einstein condensate. A general relation between the time-dependent decay-law of the system and its quantum reflection amplitude allows us to explain the quantum reflection anomaly of Bose-Einstein condensates present in BEC-surface systems as a direct consequence of the repulsive particle interaction.

quant-ph↗
arXiv2008

Generalized grand-canonical ensemble theory for interacting Bose-Einstein systems

We use the maximum information principle to include particle-interaction into the grand-canonical theory of BECs. The inclusion of the particle-interaction elucidates why thermodynamic calculations for BECs by the grand-canonical ensemble for the non-interacting case are in coincidence with up to date experimental results. However, in our generalized theory we can show that a BEC experiences a real and abrupt phase-transition in contrast to the smooth phase-transition predicted by the non-interacting grand-canonical ensemble. In addition, we discuss possible effects due to a thermal environment and the experimental probing from a general point of view.

cond-mat.stat-mech↗
arXiv2008

Trapping cold Atoms by Quantum Reflection

We examine the properties of a quantum reflection trap when particle-interaction is included. We explore the influence of the particle-interaction on the trapping for different regimes: repulsive particle-interaction and attractive particle-interaction in its stable and unstable limit. With variational techniques, we calculate the phase-diagram of the quatum reflection trap and determine the stable and unstable regimes of the system.

quant-ph↗
arXiv2006

Quantum Mechanics from the Hamilton-Jacobi Point of View

In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their description of physical systems, but differ in their descriptive manner. As a main result, a wave function in Hamilton-Jacobi theory can be decomposed into travelling waves in any point in space, not only asymptotically. The well known WKB-theory will be a special result of the more general theory, we will develop below. By the example of the linear potential and the harmonic oscillator, we will discuss quantum mechanics from the Hamilton-Jacobi point of view. Soft boundary value problems as the connection problem can be solved exactely. Quantizised energies and Maslov-indices can be calculated directely without orthonormalizing wave-functions. Also, we will focus on trajectory themes, which, in contrast to the Schroedinger point of view, follow naturally from the quantum mechanical action function.

quant-ph↗