Search results for "Mathematica"
showing 10 items of 7971 documents
Frictional quantum decoherence
2007
The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat initial state. Dependence on the diffusive terms present in the master equation is discussed with reference to both the coordinate and momentum representations.
Resonant Transitions Due to Changing Boundaries
2019
The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (\lq pantography\rq). The presence of resonant transitions involving the natural transition frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in dept, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.
Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths
2009
The dynamics of two interacting spins coupled to separate bosonic baths is studied. An analytical solution in Born approximation for arbitrary spectral density functions of the bosonic environments is found. It is shown that in the non-Markovian cases concurrence "lives" longer or reaches greater values.
Cauchy flights in confining potentials
2009
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target pdf (eventually asymptotic) equals the preselected one. To this end, dynamically distinct jump-type processes can be employed. We demonstrate that one "targeted stochasticity" scenario involves Langevin systems with a symmetric stable noise. Another derives from the L\'evy-Schr\"odinger semigroup dynamics (closely linked with topologically induced super-diffusions), which has no standard Langevin representation. For computational and visualiz…
Reading a Qubit Quantum State with a Quantum Meter: Time Unfolding of Quantum Darwinism and Quantum Information Flux
2019
Quantum non-Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non-Markovian and non-darwinistic behaviours.
High-Temperature Series Analysis of the Free Energy and Susceptibility of the 2D Random-Bond Ising Model
1999
We derive high-temperature series expansions for the free energy and susceptibility of the two-dimensional random-bond Ising model with a symmetric bimodal distribution of two positive coupling strengths J_1 and J_2 and study the influence of the quenched, random bond-disorder on the critical behavior of the model. By analysing the series expansions over a wide range of coupling ratios J_2/J_1, covering the crossover from weak to strong disorder, we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form $\chi \sim t^{-7/4} |\ln t|^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig. For the specific heat our results are less…
Linear pseudo-fermions
2012
In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with quasi-hermitian quantum mechanics. Here we repeat a similar analysis starting with the canonical anticommutation relations. We will show that in this case most of the assumptions needed in the former situation are automatically satisfied, making our construction rather {\em friendly}. We discuss some examples of our construction, again related to quasi-hermitian quantum mechanics, and the bi-coherent states for the system.
Time-dependent perturbation treatment of independent Raman schemes
2007
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.
On form-factor expansions for the XXZ chain in the massive regime
2014
We study the large-volume-$L$ limit of form factors of the longitudinal spin operators for the XXZ spin-$1/2$ chain in the massive regime. We find that the individual form factors decay as $L^{-n}$, $n$ being an even integer counting the number of physical excitations -- the holes -- that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin-spin correlation functions in the thermodynamic limit $L\rightarrow +\infty$. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.
Thermalization of Random Motion in Weakly Confining Potentials
2010
We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approa…