An odd feature of the `most classical' states of $SU(2)$ invariant
quantum mechanical systems
- URL: http://arxiv.org/abs/2106.08695v4
- Date: Wed, 8 Mar 2023 12:54:07 GMT
- Title: An odd feature of the `most classical' states of $SU(2)$ invariant
quantum mechanical systems
- Authors: L\'aszl\'o B. Szabados
- Abstract summary: Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems.
The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between the two angular momentum components and the other is the quotient of the two standard deviations.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Complex and spinorial techniques of general relativity are used to determine
all the states of the $SU(2)$ invariant quantum mechanical systems in which the
equality holds in the uncertainty relations for the components of the angular
momentum vector operator in two given directions. The expectation values depend
on a discrete quantum number and two parameters, one of them is the angle
between the two angular momentum components and the other is the quotient of
the two standard deviations. Allowing the angle between the two angular
momentum components to be arbitrary, \emph{a new genuine quantum mechanical
phenomenon emerges}: It is shown that although the standard deviations change
continuously, one of the expectation values changes \emph{discontinuously} on
this parameter space. Since physically neither of the angular momentum
components is distinguished over the other, this discontinuity suggests that
the genuine parameter space must be a \emph{double cover} of this classical
one: It must be diffeomorphic to a \emph{Riemann surface} known in connection
with the complex function $\sqrt{z}$. Moreover, the angle between the angular
momentum components plays the role of the parameter of an interpolation between
the continuous range of the expectation values found in the special case of the
orthogonal angular momentum components and the discrete point spectrum of one
angular momentum component. The consequences in the \emph{simultaneous}
measurements of these angular momentum components are also discussed briefly.
Related papers
- Corner Charge Fluctuations and Many-Body Quantum Geometry [5.795142538204481]
In many-body systems with U(1) global symmetry, the charge fluctuations in a subregion reveal important insights into entanglement and other global properties.
We demonstrate that this simple formula is insufficient for charge insulators, including composite fermi liquids.
We find that a broad class of fractional quantum Hall wavefunctions, including unprojected parton states and composite-fermion Fermi sea wavefunctions, saturates the bounds.
arXiv Detail & Related papers (2024-08-28T18:00:28Z) - Spontaneous polarized phase transitions and symmetry breaking of an ultracold atomic ensemble in a Raman-assisted cavity [9.354561963143967]
We investigate an ensemble consisting of $N$ four-level atoms within an optical cavity coupled to the single cavity mode and external laser fields.
Some novel phases characterized by the phase differences between the polarized cavity field or the atomic spin excitation and the Raman laser are found analytically.
It is found that besides the continuous $U(1)$ and discrete $mathbbZ$ symmetries, the system also exhibits two reflection symmetries $sigma_v$s, a central symmetry $C$ in the abstract position-momentum representation, and a discrete reflection-time symmetry
arXiv Detail & Related papers (2024-08-19T16:10:47Z) - Unifying uncertainties for rotor-like quantum systems [0.0]
The quantum rotor represents the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum.
We argue that the model of quantum rotor extends beyond its mechanical meaning with promising applications in the fields of singular optics, super-conductive circuits with a Josephson junction or optimal pulse shaping in the time-frequency domain.
arXiv Detail & Related papers (2024-03-04T21:44:49Z) - Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator [8.84834042985207]
We propose a fermionic extension of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian.
The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump.
arXiv Detail & Related papers (2024-01-30T17:20:34Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - Non-inertial effects on a non-relativistic quantum harmonic oscillator
in the presence of a screw dislocation [0.0]
We investigate non-inertial effects induced by a rotating frame on a non-relativistic quantum harmonic oscillator.
The presence of the topological defect (screw dislocation) as well as the fact that we are analysing the system from the point of view of a rotating frame, changes the solutions of Schr"odinger equation.
arXiv Detail & Related papers (2022-10-04T13:50:54Z) - Detecting bulk and edge exceptional points in non-Hermitian systems
through generalized Petermann factors [7.371841894852217]
Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena.
We introduce an interesting quantity (denoted as $eta$) as a new variant of the Petermann factor to measure non-unitarity.
arXiv Detail & Related papers (2022-08-31T16:24:03Z) - Three-space from quantum mechanics [0.0]
The spin geometry of Penrose is extended from $SU(2)$ to $E(3)$ (Euclidean) invariant elementary quantum mechanical systems.
The emphdistance between the centre-of-mass lines of the elementary subsystems of a classical composite system can be recovered from their emphrelative orbital angular momenta by $E(3)$-invariant classical observables.
arXiv Detail & Related papers (2022-03-09T15:59:47Z) - Quantum Entanglement of Non-Hermitian Quasicrystals [7.371841894852217]
We present a class of experimentally realizable models for non-Hermitian quasicrystal chains.
We numerically determine the metal-insulator transition point.
Inspired by entanglement spectrum, we further analytically prove that a duality exists between the two phase regions.
arXiv Detail & Related papers (2021-12-26T16:17:04Z) - The 'most classical' states of Euclidean invariant elementary quantum
mechanical systems [0.0]
Complex techniques of general relativity are used to determine emphall the states in the two and three dimensional momentum spaces.
The existence of such states depends not only on the Lie algebra, but on the choice for its generators as well.
arXiv Detail & Related papers (2021-11-22T15:08:56Z) - $\mathcal{PT}$-symmetry in compact phase space for a linear Hamiltonian [0.0]
We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact.
We analyze how the non-Hermitian part of the Hamiltonian affects the time evolution of two archetypical quantum states, coherent and Dicke states.
arXiv Detail & Related papers (2020-07-30T20:38:00Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.