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Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
In this work, we solve the fundamental problem of describing the coordinate transformations that preserve the upper triangular Toeplitz form of the given operator field. Surprisingly, this problem is closely related to the description of…
In this paper, we investigate the Hautus test for evolution equation with the operators depending on time.
We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
We prove the boundedness of a trilinear operator that is modulation invariant and which contains curvature information given by the presence of a complex exponential, adding to the small class of examples of such operators.
The NLO evolution equations for quadrupole and double dipole operators have been obtained within the high energy operator expansion method. The corresponding quasi-conformal evolution equations for the composite operators were constructed.
The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution…
In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
The time-evolution operator corresponding to the fractional-time Schr\"odinger equation is nonunitary because it fails to preserve the norm of the vector state in the course of its evolution. However, in the context of the time-dependent…
In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are…
We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
Some mechanical systems with dissipation can be described within the framework of the so-called contact mechanics: a modified form of the Euler-Lagrange equations stemming from Herglotz's variational principle, which admits a geometric…
For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our…