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In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal…

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical…

We construct defects in the XXZ and sine-Gordon models by making use of the representation theory of quantum affine sl_2. The representations involved are generalisations of the infinite-dimensional, q-oscillator representations used in the…

We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…

We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…

Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this…

A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…

The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for…

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial…

This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians…

A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…

Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…

Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator…

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate…

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…