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It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is…
We derive a uniqueness result for non-Cartesian composition of systems in a large class of process theories, with important implications for quantum theory and linguistics. Specifically, we consider theories of wavefunctions valued in…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
By analytically continuing the eigenvalue problem of a system of two coupled harmonic oscillators in the complex coupling constant $g$, we have found a continuation structure through which the conventional ground state of the decoupled…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the…
We investigate refined algebraic quantisation of the constrained Hamiltonian system introduced by Boulware as a simplified version of the Ashtekar-Horowitz model. The dimension of the physical Hilbert space is finite and asymptotes in the…
This is an elaboration about the "extra" advantage of the performance of quantized physical systems over classical ones; both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based upon…
Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
A self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
Relative to a given factoring of the Hilbert space, the decomposition of an operator into a convex sum of products over sets of distinct 1-projectors, one set linearly independent, is unique.
We show that the dissipation term in the Hamiltonian for a couple of classical damped-amplified oscillators manifests itself as a geometric phase and is actually responsible for the appearance of the zero point energy in the quantum…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…