Related papers: Analytic Representation of Finite Quantum Systems
We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be…
The $L^2$-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the $L^2$-zeta…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding…
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total…
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 use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.
Free coherent states for a system with two degrees of freedom is defined. An isomorphism of the space of distributions on 2-adic disc and the space of free coherent states is constructed.
While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
It is known that a semi-classical analysis is not always adequate for atomtronics devices, but that a fully quantum analysis is often necessary to make reliable predictions. While small numbers of atoms at a small number of sites are…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
We study dynamics of an artificial two-level atom in an open 1D space by measuring evolution of its coherent and incoherent emission. States of the atom -- a superconducting flux qubit coupled to a transmission line -- are fully controlled…
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…