scholarly journals Parameterizing qudit states

2021 ◽  
Vol 29 (4) ◽  
pp. 361-386
Author(s):  
Arsen Khvedelidze ◽  
Dimitar Mladenov ◽  
Astghik Torosyan
Keyword(s):  
State Space ◽  
Particle Physics ◽  
Convex Geometry ◽  
Orbit Space ◽  
Quantum Systems ◽  
Physical Models ◽  
General Situation ◽  
Elementary Particle Physics ◽  
Primary Element ◽  
Unitary Orbit

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

scholarly journals Multimessenger Probes for New Physics in Light of A. Sakharov’s Legacy in Cosmoparticle Physics

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 222
Author(s):  
Maxim Khlopov
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
New Physics ◽  
Physical Models ◽  
Beyond The Standard Model ◽  
Fundamental Relationship ◽  
Relationship Of ◽  
The Universe ◽  
Selection Of

A.D. Sakharov’s legacy in now standard model of the Universe is not reduced to baryosynthesis but extends to the foundation of cosmoparticle physics, which studies the fundamental relationship of cosmology and particle physics. Development of cosmoparticle physics involves cross-disciplinary physical, astrophysical and cosmological studies of physics Beyond the Standard model (BSM) of elementary particles. To probe physical models for inflation, baryosynthesis and dark matter cosmoparticle physics pays special attention to model dependent messengers of the corresponding models, making their tests possible. Positive evidence for such exotic phenomena as nuclear interacting dark atoms, primordial black holes or antimatter globular cluster in our galaxy would provide the selection of viable BSM models determination of their parameters.

scholarly journals Dynamical Symmetries of the H Atom, One of the Most Important Tools of Modern Physics: SO(4) to SO(4,2), Background, Theory, and Use in Calculating Radiative Shifts

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1323 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Hydrogen Atom ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Bound States ◽  
Integrated Treatment ◽  
Invariance Group ◽  
Elementary Particle Physics ◽  
Background Theory ◽  
Modern Physics ◽  
History Of

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review, we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1), and the expanded group SO(4,2). After giving a brief history of these discoveries, most of which took place from 1935–1975, we focus on the physics of the hydrogen atom, providing a background discussion of the symmetries, providing explicit expressions for all of the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions that have the same quantum numbers as the ordinary bound states. We present some new results from SO(4,2) group theory that are useful in a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts, and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

Notes on Elementary Particle Physics

1972 ◽  
Vol 40 (11) ◽  
pp. 1720-1721
Author(s):  
H. Muirhead ◽  
Richard A. Morrow
Keyword(s):  
Elementary Particle ◽  
Particle Physics ◽  
Elementary Particle Physics
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