Symmetry In Quantum Mechanics Research Articles

RETRACTED: Bracken, P. Envariance as a Symmetry in Quantum Mechanics and Applications to Statistical Mechanics. Symmetry 2023, 15, 1923

The Symmetry Editorial Office retracts the article titled “Envariance as a Symmetry in Quantum Mechanics and Applications to Statistical Mechanics” [...]

Bright–dark envelope-optical solitons in space-time reverse generalized Fokas–Lenells equation: Modulated wave gain

Here, we investigate the impact of space-time reverse (STR) problems, a result of parity-time symmetry in optics and quantum mechanics, on soliton propagation in optical fibers. The STR problems are characterized by the existence of a field and its reverse. The research introduces a new classification of two scenarios: non-interactive and interactive fields and reverse fields. The solutions for the generalized Fokas–Lenells equation (gFLE) with STR and third-order dispersion are derived. To tackle this, adaptive transformations for the field and its reverse are introduced, employing a unified method. In the non-interactive scenario, both exact and approximate solutions are found. However, in the interactive case, only exact solutions are discovered. This work reveals that the presence of the field and its reverse unveils new soliton structures, including bright–dark envelope solitons and right and left envelope-solitons. In the non-interactive case, the field displays a right envelope-soliton, while the reverse field exhibits a left envelope-soliton (or vice versa). The study hypothesizes that the presence of a reverse field might impede soliton propagation in optical fibers. The research also includes an analysis of modulation instability (MI), determining that MI is initiated when the coefficient of Raman scattering exceeds a critical value. Furthermore, the study examines the modulated wave gain and explores global bifurcation through phase portrait by constructing the Hamiltonian function.

Envariance symmetry in quantum mechanics and statistical mechanics

Envariance symmetry in quantum mechanics and statistical mechanics

States, observables and symmetries in p-adic quantum mechanics

In the framework of quantum mechanics constructed over a quadratic extension of the field of p-adic numbers, we consider an algebraic definition of physical states. Next, the corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a p-adic counterpart of the POVMs associated with a quantum system over the complex numbers. Differently from the standard complex setting, the space of all states of a p-adic quantum system has an affine — rather than convex — structure. Thus, a symmetry transformation may be defined, in a natural way, as a map preserving this affine structure. We argue that the group of all symmetry transformations of a p-adic quantum system has a richer structure wrt the case of standard quantum mechanics over the complex numbers.

Galilean relativity and the path integral formalism in quantum mechanics

Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of Galilean transformations. In quantum mechanics, Galilean boosts require a non-trivial transformation rule for the wave function and a concomitant “projective representation” of the Galilean symmetry group. Using Feynman's path integral formalism, this latter result can be shown to be equivalent to the non-invariance of the Lagrangian. Thus, using path integral methods, the representation of certain symmetry groups in quantum mechanics can be simply understood in terms of the transformation properties of the classical Lagrangian and conversely. The main results reported here should be accessible to students and teachers of physics—particularly classical mechanics, quantum mechanics, and mathematical physics—at the advanced undergraduate and beginning graduate levels, providing a useful exposition for those wanting to explore topics such as the path integral formalism for quantum mechanics, relativity principles, Lagrangian mechanics, and representations of symmetries in classical and quantum mechanics.

RETRACTED: Envariance as a Symmetry in Quantum Mechanics and Applications to Statistical Mechanics

A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal in number to that of the possible outcomes of the experiment. Correlations between the apparatus and environment give rise to a type of selection rule which prohibits the apparatus from appearing in a superposition corresponding to different eigenvalues of the pointer basis of the apparatus. The eigenspaces of this observable form a natural basis for the apparatus and determine the observable of the measured quantum system. It is also discussed how statistical mechanics can be formulated in terms of this symmetry.

Mathcal{N} = 4 SYM, (super)-polynomial rings and emergent quantum mechanical symmetries

The structure of half-BPS representations of psu(2, 2|4) leads to the definition of a super-polynomial ring mathcal{R} (8|8) which admits a realisation of psu(2, 2|4) in terms of differential operators on the super-ring. The character of the half-BPS fundamental field representation encodes the resolution of the representation in terms of an exact sequence of modules of mathcal{R} (8|8). The half-BPS representation is realized by quotienting the super-ring by a quadratic ideal, equivalently by setting to zero certain quadratic polynomials in the generators of the super-ring. This description of the half-BPS fundamental field irreducible representation of psu(2, 2|4) in terms of a super-polynomial ring is an example of a more general construction of lowest-weight representations of Lie (super-) algebras using polynomial rings generated by a commuting subspace of the standard raising operators, corresponding to positive roots of the Lie (super-) algebra. We illustrate the construction using simple examples of representations of su(3) and su(4). These results lead to the definition of a notion of quantum mechanical emergence for oscillator realisations of symmetries, which is based on ideals in the ring of polynomials in the creation operators.

Symmetry-induced decoherence-free subspaces

Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global classes of decoherence-free subspaces for many-body systems through the introduction of "ghost variables". The latter are orthogonal to the symmetry and the coupling to the environment does not depend on them. Constructing them is facilitated in classical phase space and can be transferred to quantum mechanics through the equivalent role that Poisson and Lie algebras play for symmetries in classical and quantum mechanics, respectively. Examples are given for an interacting spin system.

Symmetry in Quantum Mechanics and Gauge Theory for Gravity

To unify gravitational interaction with other three kinds of interaction are a work hadn’t been finished by Albert Einstein and a big problem that human must solve to continue living in the universe.

Complex-self-adjointness

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions, and antilinear eigenfunction expansions. The study is motivated by physical symmetries in quantum mechanics with non-self-adjoint operators.

Quantum Algorithms for Testing Hamiltonian Symmetry.

Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this Letter, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.

Brukner-Zeilinger invariant information in the presence of conjugate symmetry

To quantify the intrinsic information content in a quantum state, Brukner and Zeilinger introduced the concept of operationally invariant information in terms of the outcome probabilities of measuring a complete set of mutually complementary observables [\ifmmode \check{C}\else \v{C}\fi{}. Brukner and A. Zeilinger, Phys. Rev. Lett. 83, 3354 (1999)]. This information quantity has basic significance and implications, and the present work is devoted to some further studies of it. We first introduce the Brukner-Zeilinger invariant information in the presence of conjugate symmetry or antisymmetry, which are motivated by considerations of fundamental issues concerning conjugate symmetry in quantum mechanics. Then we prove that both the Brukner-Zeilinger invariant information with conjugate symmetry and that with conjugate antisymmetry are convex in the quantum state, and we show that they constitute a natural decomposition of the Brukner-Zeilinger invariant information. We further relate them to the imaginarity (i.e., the usage of a complex number field) of quantum mechanics and evaluate their extreme values.

Special Issue: “Symmetries in Quantum Mechanics and Statistical Physics”

Symmetry is a fundamental concept in science and has played a significant role since the early days of quantum physics [...]

PT symmetry and the evolution speed in open quantum systems 1

The dynamics of an open quantum system with balanced gain and loss is not described by a PT-symmetric Hamiltonian but rather by Lindblad operators. Nevertheless the phenomenon of PT-symmetry breaking and the impact of exceptional points can be observed in the Lindbladean dynamics. Here we briefly review the development of PT symmetry in quantum mechanics, and the characterisation of PT-symmetry breaking in open quantum systems in terms of the behaviour of the speed of evolution of the state.

Special Issue: “Symmetries in Quantum Mechanics”

This Special Issue “Symmetries in Quantum Mechanics” describes research using two of the most fundamental probes we have in nature [...]

Power Law Duality in Classical and Quantum Mechanics

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.

Electrically injected parity-time symmetric distributed feedback laser diodes (DFB) for telecom applications

Abstract The new paradigm of parity-time symmetry in quantum mechanics has readily been applied in the field of optics with numerous demonstrations of exotic properties in photonic systems. In this work, we report on the implementation of single frequency electrically injected distributed feedback (DFB) laser diodes based on parity-time symmetric dual gratings in a standard ridge waveguide configuration. We demonstrate enhanced modal discrimination for these devices as compared with index or gain coupled ones, fabricated in the same technology run. Optical transmission probing experiments further show asymmetric amplification in the light propagation confirming the parity-time symmetry signature of unidirectional light behavior. Another asset of these complex coupled devices is further highlighted in terms of robustness to optical feedback.

Entanglement fidelity ratio for elastic collisions in non-ideal two-temperature dense plasma

The quantum diffraction and symmetry effects on the entanglement fidelity (EF) of different elastic electron–electron, ion–ion and electron–ion interactions are investigated in non-ideal dense plasmas. The partial wave analysis, an effective screened interaction potential including quantum mechanical diffraction and symmetry effects are employed to obtain the EF in a non-ideal dense plasma. We show that collision energy and temperatures of electron and ion have destructive effects on the entanglement in the system. In fact, by decreasing the temperature of plasma particles, the quantum effects become more prominent and the entanglement is elevated. Also, increase in the density of plasma leads to the enhancement of entanglement ratio. Additionally, some important characteristic parameters of the scattering such as differential, transport and total cross sections are calculated.

Parity–Time Symmetry Synthetic Lasers: Physics and Devices

AbstractThe invention of the laser has revolutionized modern science and engineering as well as our daily lives. Recently, a new class of lasers based on concepts borrowed from parity–time symmetry in quantum mechanics has emerged. Parity–time symmetry, initially applied to condensed matter systems, extends canonical quantum theory to non‐Hermitian quantum theory. The experimental exploration of parity–time symmetry in electronics is challenging; so by analogy, such concept is introduced in photonics where flexibility exists in realizing non‐Hermitian eigenstates involving optical gain and loss. Lasers intrinsically involve both gain and loss, which makes them the natural candidates to explore and exploit parity–time symmetry in photonics. Recent studies have demonstrated various novel laser devices based on parity–time symmetry, which show unique properties such as single mode lasing, chiral mode lasing, and exceptional point enhanced sensing. In this review, the fundamentals are introduced and recent advances in parity–time symmetric laser devices are discussed, furthermore an outlook on this emergent field is provided.

STRUCTURAL PROPERTIES OF HYDROGEN PLASMA

This paper considers hydrogen, non-ideal plasma. The structural properties of such plasma were investigated. To study properties of plasma, effective potentials describing the interaction between particles were used. These potentials take into account various effects: screening and quantum-mechanical (diffraction and symmetry). The Pauli exclusion principle prohibits the simultaneous presence of two identical particles with a half-integer spin (in this case, electrons) in the same state. Pair correlation functions were calculated in hyper-netted chain approximation for the integral equation of the Ornstein-Zernike on the basis of the interaction potentials. The symmetry effect is more pronounced at short distances and for higher values of density. The antiparallel direction of the electron spins increases the probability of finding electrons at distance R from each other, the parallel direction decreases this probability due to the prohibition of the presence of two electrons with the same spins in the same state.