Irreversible quantum dynamics and the Hilbert space structure of quantum kinematics

1983 ◽  
Vol 24 (7) ◽  
pp. 1779-1782 ◽  
Author(s):  
N. Gisin
Keyword(s):  
Hilbert Space ◽  
Quantum Dynamics ◽  
Space Structure ◽  
Irreversible Quantum Dynamics

scholarly journals Real algebras with a Hilbert space structure

1966 ◽  
Vol 6 (4-5) ◽  
pp. 459-465
Author(s):  
Lars Ingelstam
Keyword(s):  
Hilbert Space ◽  
Space Structure ◽  
Real Algebras

scholarly journals A simple characterization of commutativeH*-algebras

1999 ◽  
Vol 22 (4) ◽  
pp. 885-888
Author(s):  
Parfeny P. Saworotnow
Keyword(s):  
Hilbert Space ◽  
Space Structure ◽  
Simple Characterization

CommutativeH*-algebras are characterized without postulating the existence of Hilbert space structure.

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 dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150155 ◽  
Author(s):  
C. M. Sánchez ◽  
P. R. Levstein ◽  
L. Buljubasich ◽  
H. M. Pastawski ◽  
A. K. Chattah
Keyword(s):  
Hilbert Space ◽  
Quantum Dynamics ◽  
Spin Systems ◽  
Equilibrium Density ◽  
Multiple Quantum ◽  
Counting Procedure ◽  
Two Samples ◽  
Spin Counting ◽  
Loschmidt Echo ◽  
The Many

In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an ‘infinite’ network. By contrast, the liquid crystal N -(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.

scholarly journals Hilbert space structure and positive operators

2005 ◽  
Vol 305 (2) ◽  
pp. 560-565 ◽  
Author(s):  
Dimosthenis Drivaliaris ◽  
Nikos Yannakakis
Keyword(s):  
Hilbert Space ◽  
Space Structure ◽  
Positive Operators

scholarly journals THE SOq(N, R)-SYMMETRIC HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE ${\bf R}_q^N$ AND ITS HILBERT SPACE STRUCTURE

1993 ◽  
Vol 08 (26) ◽  
pp. 4679-4729 ◽  
Author(s):  
GAETANO FIORE
Keyword(s):  
Hilbert Space ◽  
Euclidean Space ◽  
Harmonic Oscillator ◽  
Mechanical Model ◽  
Scalar Product ◽  
Space Structure ◽  
Quantum Mechanical ◽  
Quantum Space ◽  
Isotropic Harmonic Oscillator ◽  
Definition Of

We show that the isotropic harmonic oscillator in the ordinary Euclidean space RN (N≥3) admits a natural q-deformation into a new quantum-mechanical model having a q-deformed symmetry (in the sense of quantum groups), SO q(N, R). The q-deformation is the consequence of replacing RN by [Formula: see text] (the corresponding quantum space). This provides an example of quantum mechanics on a noncommutative geometrical space. To reach the goal, we also have to deal with a sensible definition of integration over [Formula: see text], which we use for the definition of the scalar product of states.

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