Related papers: Generalized variational procedure: An application …
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and…
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in…
Generalised Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalised Dyson boson-fermion mapping is a…
A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence…
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit…
A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…
We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with $\mathbb{S}^1 -$symmetry.…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb-Breit Hamiltonian aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei…
A new method to work out the Hermitian correspondence of a PT-symmetric quantum mechanical Hamiltonian is proposed. In contrast to the conventional method, the new method ends with a local Hamiltonian of the form p^2/2+m^2x^2/2+v(x) without…
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of…
We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $\mathcal{PT}$-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the…
Generalized parton distributions (GPDs) are studied at the hadronic (nonperturbative) scale within different assumptions based on a relativistic constituent quark model. In particular, by means of a meson-cloud model we investigate the role…
We derive the exact form of the bosonized Hamiltonian for a many-body fermion system in one spatial dimension with arbitrary dispersion relations, using the droplet bosonization method. For a single-particle Hamiltonian polynomial in the…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…