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Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Using the squeezed state formalism the coherent state representation of quantum fluctuations in an expanding universe is derived. It is shown that this provides a useful alternative to the Wigner function as a phase space representation of…
A method based on integrals of motion for collective processes has been introduced to achieve physical schemes in which one of the systems is insensitive to interaction. Decoherence-free quantum channels that allow sending any state of…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Systems of Newton equations of the form $\ddot{q}=-{1/2}A^{-1}(q)\nabla k$ with an integral of motion quadratic in velocities are studied. These equations generalize the potential case (when A=I, the identity matrix) and they admit a…
We define quantum field theory by taking the Lagrangian action to be given as a sequence of mathematically well-defined functionals written in terms of operator fields fulfilling given \hbox{local} commutation relations. The renormalized…
Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the…
An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed…
The ability to control the motion of mechanical systems through its interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
A Lagrangian description is presented which can be used in conjunction with particle interpretations of quantum mechanics. A special example of such an interpretation is the well-known Bohm model. The Lagrangian density introduced here also…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic…
By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…