相关论文: Symmetries Shared by Particle Physics and Quantum …
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
The non-relativistic hydrogen atom and the Zwanziger problem have the same dynamical symmetry for bound and scattering states.We show that this is also true for a Hilbert space which is non-commutative in co-ordinates. The group structure…
We investigate quantum properties of light in optical parametric oscillators (OPOs) based on four-wave mixing gain in media with third-order non-linearities. In spite of other competing $\chi^{(3)}$ effects, such as phase modulation,…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
The quark masses evaluated by the Particle Data Group are consistent with terms in a geometric progression of mass values descending from the Planck Mass. The common ratio of the sequence is 2/pi. The quarks occupy the 'principal' levels of…
We discuss some applications of higher symmetry groups to condensed matter systems. We give special attention to the groups SO(n) (n = 4, 5, 6, 8) in the two-dimensional Hubbard model and its generalizations, which model the high T_c…
In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem…
We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and…
The unitary irreducible representations of the covering group of the Poincare group P define the framework for much of particle physics on the physical Minkowski space P/L, where L is the Lorentz group. While extraordinarily successful, it…
Parity-Time ($\mathcal{PT}$) symmetry has become an important concept in the design of synthetic optical materials, with exotic functionalities such as unidirectional transport and non-reciprocal reflection. At exceptional points, this…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be…
We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell…
Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasi-triangular Hopf algebras). In this letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it…
The problem of quantizing the canonical pair angle and action variables phi and I is almost as old as quantum mechanics itself and since decades a strongly debated but still unresolved issue in quantum optics. The present paper proposes a…
The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed…
Light is known to exhibit quantum uncertainty in terms of its amplitude, phase, and polarization. However, quantum uncertainty related to coherence, which is also a fundamental physical property of light, has not been considered to date.…
Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…
The entanglement of multi-atom quantum states is considered. In order to cancel noise due to inhomogeneous light atom coupling, the concept of matched multi-atom observables is proposed. As a means to eliminate an important form of…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…