Related papers: Back and forth from Fock space to Hilbert space: a…
Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Efficient encoding of electronic operators into qubits is essential for quantum chemistry simulations. The majority of methods map single electron states to qubits, effectively handling electron interactions. Alternatively, pairs of…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
In this paper, we review two approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
The manipulation of distinct degrees of freedom of photons plays a critical role in both classical and quantum information processing. While the principles of wave optics provide elegant and scalable control over classical light in spatial…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
Recent developments of experimental techniques in the field of ultra-cold gases open a path to study the crossover from 'few' to 'many' on the quantum level. In this case, accurate description of inter-particle correlations is very…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…