scholarly journals Supersymmetry and Exceptional Points

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 892 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Energy Levels ◽  
Harmonic Oscillators ◽  
Exceptional Point ◽  
Basic Principles ◽  
Exceptional Points ◽  
Super Symmetry ◽  
Physical Literature

The phenomenon of degeneracy of energy levels is often attributed either to an underlying (super)symmetry (SUSY), or to the presence of a Kato exceptional point (EP). In our paper a conceptual bridge between the two notions is proposed to be provided by the recent upgrade of the basic principles of quantum theory called, equivalently, PT − symmetric or three-Hilbert-space (3HS) or quasi-Hermitian formulation in the current physical literature. Although the original purpose of the 3HS approach laid in the mere simplification of technicalities, it is shown here to serve also as a natural theoretical link between the apparently remote concepts of EPs and SUSY. An explicit illustration of their close mutual interplay is provided by the description of infinitely many supersymmetric, mutually non-equivalent and EP-separated regularized spiked harmonic oscillators.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

Functional Quantum Theory of Free Relativistic Fermi Fields

1970 ◽  
Vol 25 (5) ◽  
pp. 575-586
Author(s):  
H. Stumpf
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Physical Interpretation ◽  
Functional Equations ◽  
Dirac Field ◽  
Functional Hilbert Space ◽  
Free Fermi ◽  
Special Case ◽  
Relativistic Fermi

Functional quantum theory of free Fermi fields is treated for the special case of a free Dirac field. All other cases run on the same pattern. Starting with the Schwinger functionals of the free Dirac field, functional equations and corresponding many particle functionals can be derived. To establish a functional quantum theory, a physical interpretation of the functionals is required. It is provided by a mapping of the physical Hilbert space into an appropriate functional Hilbert space, which is introduced here. Mathematical details, especially the problems connected with anticommuting functional sources are treated in the appendices.

The Hydrogen Bond

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Marc Henry
Keyword(s):  
Hydrogen Bond ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Energy Levels ◽  
Strong Association ◽  
Emergent Property ◽  
Water Molecules ◽  
Linear Coupling ◽  
Non Linear

The claim that chemistry has been explained in terms of quantum theory is received wisdom. Yet quantum physics is unable to explain the strong association of water molecules in liquid or ice. Marc Henry suggests the hydrogen bond is an emergent property of matter resulting from a non-linear coupling between quantified energy levels of water molecules and a quantified internal electromagnetic field.

Exceptional points in 1D arrays of quantum harmonic oscillators

2019 ◽  
Vol 127 (2) ◽  
pp. 20001 ◽  
Author(s):  
A. Cabot ◽  
G. L. Giorgi ◽  
S. Longhi ◽  
R. Zambrini
Keyword(s):  
Harmonic Oscillators ◽  
Exceptional Points

scholarly journals Space-time from Collapse of the Wave-function

2019 ◽  
Vol 74 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Quantum Theory ◽  
Minkowski Space ◽  
Time Scales ◽  
Quantum Interference ◽  
Quantum Dynamics ◽  
Space Time ◽  
Minkowski Space Time ◽  
Macroscopic Objects

AbstractWe propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then propose such a formulation by invoking an operator Minkowski space-time on the Hilbert space. We suggest relativistic spontaneous localisation as the mechanism for recovering classical space-time from the underlying theory. Quantum interference in time could be one possible signature for operator time, and in fact may have been already observed in the laboratory, on attosecond time scales. A possible prediction of our work seems to be that interference in time will not be seen for ‘time slit’ separations significantly larger than 100 attosecond, if the ideas of operator time and relativistic spontaneous localisation are correct.

scholarly journals Quantum Theory in Pseudo-Hilbert Space. II

1959 ◽  
Vol 21 (5) ◽  
pp. 727-730 ◽  
Author(s):  
Gaku Konisi ◽  
Takesi Ogimoto
Keyword(s):  
Hilbert Space ◽  
Quantum Theory

INVARIANT EIGEN-OPERATOR METHOD FOR SOLVING ENERGY GAP FOR SOME HAMILTONIANS IN MOLECULAR PHYSICS

2007 ◽  
Vol 21 (12) ◽  
pp. 1961-1969 ◽  
Author(s):  
HONG-YI FAN ◽  
TONG-TONG WANG
Keyword(s):  
Energy Gap ◽  
Molecular Model ◽  
Energy Levels ◽  
Linear Chain ◽  
Operator Method ◽  
Harmonic Oscillators ◽  
Molecular Physics ◽  
Coupled Harmonic Oscillators ◽  
Diagonalization Method

We show that the recently proposed invariant eigen-operator method is particularly applicable to solving the energy levels for some Hamiltonians in molecular physics. These are tri-atom molecules, the identical d-dimensional coupled harmonic oscillators and the dissipative linear-chain molecular model etc. The calculation is more direct and simpler than the usual diagonalization method for dynamic Hamiltonians.

Sign in / Sign up

Export Citation Format

Share Document