Related papers: Grassmann Variables and the Jaynes-Cummings Model
The Fokker-Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov-Johnson-Mehl-Avrami) transformations. The classical case of transformations…
We consider a variation of $O(N)$-symmetric vector models in which the vector components are Grassmann numbers. We show that these theories generate the same sort of random polymer models as the $O(N)$ vector models and that they lie in the…
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes-Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation…
The anticommuting analysis with Grassmann variables is applied to the two-dimensional Ising model in statistical mechanics. The discussion includes the transformation of the partition function into a Gaussian fermionic integral, the…
Among the best known quantities obtainable from photon correlation measurements are the $g^{(m)}$~correlation functions. Here, we introduce a new procedure to evaluate these correlation functions based on higher-order factorial cumulants…
Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
Quantum generative modeling is emerging as a powerful tool for advancing data analysis in high-energy physics, where complex multivariate distributions are common. However, efficiently learning and sampling these distributions remains…
Under low-collisionality conditions the isotropic part of the electron velocity distribution function in a plasma becomes non-local and the electrons can be described by a single global distribution function . This is also the regime…
We present a mathematical procedure which leads us to obtain analytical solutions for the atomic inversion and Wigner function in the framework of the Jaynes-Cummings model with an external quantum field, for any kinds of cavity and driving…
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…
We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general…
We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes-Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference…
This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input…
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and…
The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in…
Dynamics of atom-field correlations and single-mode nonclassicalities present in the resonant Jaynes-Cummings model are investigated using negativity and entanglement potential for a set of initial states. The study has revealed the…
After a short outline of the factorization and Grassmann picture of the one-dimensional (1D) Fokker-Planck (FP) equation, we consider a class of spatially-inhomogeneous solutions of the 2D FP equation with symmetric 2D (super)potentials. We…
This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field…