Related papers: Herman-Kluk-Like Semi-Classical Initial-Value Repr…
The systems with small binding energies and widely distributed in space bound-state wave functions are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of…
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…
Calculations at finite temperatures are fundamental in different scientific fields, from nuclear physics to condensed matter. Evolution in imaginary time is a prominent classical technique for preparing thermal states of quantum systems. We…
In this work, we investigate a theory of stochastic integration for operator-valued processes with respect to semimartingales taking values in the dual of a nuclear space. Our construction of this particular stochastic integral relies on…
We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat…
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available…
We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become…
One of the useful and practical methods for solving quantum-mechanical many-body systems is to recast the full problem into a form of the effective interaction acting within a model space of tractable size. Many of the effective-interaction…
We report on a nontrivial bosonization scheme for spin operators. It is shown that in the large $N$ limit, at infinite temperature, the operators $\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$ behave like the creation and annihilation operators,…
Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum…
We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a…
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of…
For the low-temperature electrical conductance of a disordered {\it quantum insulator} in $d$-dimensions, Mott \cite{mott} had proposed his Variable Range Hopping (VRH) formula, $G(T) = G_0 {\rm exp}[-(T_0/T)^{\gamma}]$, where $G_0$ is a…
In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification of…
We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…
By use of the recently derived $universal$ discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically, and evaluated numerically at each imaginary time step, for…
Harmonic wave functions for integer and half-integer angular momentum are given in terms of the Euler angles $(\theta,\phi,\psi)$ that define a rotation in $SO(3)$, and the Euclidean norm in ${\mathbb R}^3$. Following a classical work by…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…