Related papers: Quaternion representation and symplectic spin tomo…
The quantum geometric tensor (QGT) embodies the geometry of the eigenstates of a system's Hamiltonian, and its full characterization across diverse quantum systems is essential. However, it is challenging to characterize the QGT of…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the…
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be…
In the first part of this paper we study minimal representations of simply connected simple split groups of type $D_k$ or $E_k$ over local non-archimedian fields. Our main result is an explicit formula for the spherical vectors in these…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…
In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly…
The invertable map of spin state density operator onto quasiprobability distribution of three continuous variables is constructed. The connection with two-mode electromagnetic field oscillators is discussed. The inversion formula for…
We present a theory of quantum optical control of an electron spin in a single semiconductor quantum dot via spin-flip Raman transitions. We show how an arbitrary spin rotation may be achieved by virtual excitation of discrete or continuum…
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
In an effort to provide an alternative method to represent a quantum spin, a precise 3D nonlinear dynamics method is used. A two-sided torque function is created to mimic the unique behavior of the quantum spin. A full 3D representation of…
A semiclassical approach is proposed to calculate the collective potential and mass parameters to formulate a collective Hamiltonian capable of describing the wobbling motion in both even-even and odd-mass systems. By diagonalizing the…
The problem of moving of a charged particle in electromagnetic field is considered in terms of tomographic probability representation. The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the…