Related papers: Hamiltonian Quantum Dynamics With Separability Con…
The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The…
We study de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants"…
Many-body wavefunctions usually lie in high-dimensional Hilbert spaces. However, physically relevant states, i.e, the eigenstates of the Schr\"odinger equation are rare. For many-body systems involving only pairwise interactions, these…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with…
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate…
We investigate the strong-field limit of a charged particle in an electromagnetic field as a toy model for general covariant systems, establishing a novel connection between constrained Hamiltonian dynamics and noncommutative geometry.…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $p=2$…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
Isolated interacting quantum systems generally thermalize, yet there are several examples for the breakdown of ergodicity, such as many-body localization and quantum scars. Recently, ergodicity breaking has been observed in systems…
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the…