scholarly journals A NOTE ON THE QUANTUM-MECHANICAL RICCI FLOW

2009 ◽  
Vol 24 (27) ◽  
pp. 4999-5006
Author(s):  
JOSÉ M. ISIDRO ◽  
J. L. G. SANTANDER ◽  
P. FERNÁNDEZ DE CÓRDOBA
Keyword(s):  
Quantum Mechanics ◽  
Configuration Space ◽  
Ricci Flow ◽  
Riemannian Metric ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Conformally Flat ◽  
Flow Equations ◽  
Emergent Quantum Mechanics

We obtain Schrödinger quantum mechanics from Perelman's functional and from the Ricci-flow equations of a conformally flat Riemannian metric on a closed two-dimensional configuration space. We explore links with the recently discussed emergent quantum mechanics.

scholarly journals On the Ricci flow and emergent quantum mechanics

2009 ◽  
Vol 174 ◽  
pp. 012033
Author(s):  
José M Isidro ◽  
J L G Santander ◽  
P Fernández de Córdoba
Keyword(s):  
Quantum Mechanics ◽  
Ricci Flow ◽  
Emergent Quantum Mechanics

scholarly journals AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250048 ◽  
Author(s):  
D. ACOSTA ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
J. M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Entropy Flow ◽  
Planck’S Constant ◽  
Formal Derivation ◽  
Usual Quantum ◽  
Holographic Screen ◽  
Holographic Screens ◽  
Planck's Constant ◽  
Emergent Quantum Mechanics

Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.

A MECHANICS FOR THE RICCI FLOW

2009 ◽  
Vol 06 (05) ◽  
pp. 759-767 ◽  
Author(s):  
S. ABRAHAM ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
JOSÉ M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Ricci Flow ◽  
Jacobi Equation ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Flow Equation ◽  
Time Dependent ◽  
Dimensional Manifold ◽  
Conformally Flat ◽  
Hamilton Jacobi Equation

We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton–Jacobi equation of the mechanics so defined.

scholarly journals QUANTUM MECHANICS AS A SPONTANEOUSLY BROKEN GAUGE THEORY ON A U(1) GERBE

2008 ◽  
Vol 05 (02) ◽  
pp. 233-252 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Gauge Symmetry ◽  
Configuration Space ◽  
Fibre Bundle ◽  
Higgs Mechanism ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Classical Action ◽  
Yang Mills

Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/ħ), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a point-by-point basis on configuration space. This is equivalent to the statement that quantum mechanics is a U(1) gauge theory. Unlike Yang–Mills theories, however, the geometry of this gauge symmetry is not given by a fibre bundle, but rather by a gerbe. Since this gauge symmetry is spontaneously broken, an analogue of the Higgs mechanism must be present. We prove that a Heisenberg-like noncommutativity for the space coordinates is responsible for the breaking. This allows to interpret the noncommutativity of space coordinates as a Higgs mechanism on the quantum-mechanical U(1) gerbe.

scholarly journals $$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Soumangsu Chakraborty ◽  
Amiya Mishra
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Partition Function ◽  
Linear Combination ◽  
Mechanical Systems ◽  
General Linear ◽  
Quantum Mechanical ◽  
Partition Functions ◽  
Flow Equations ◽  
Quantum Mechanical Systems

Abstract In this paper, we continue the study of $$ T\overline{T} $$ T T ¯ deformation in d = 1 quantum mechanical systems and propose possible analogues of $$ J\overline{T} $$ J T ¯ deformation and deformation by a general linear combination of $$ T\overline{T} $$ T T ¯ and $$ J\overline{T} $$ J T ¯ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and U(1) gauge theory.

scholarly journals RICCI FLOW, QUANTUM MECHANICS AND GRAVITY

2009 ◽  
Vol 06 (03) ◽  
pp. 505-512
Author(s):  
JOSÉ M. ISIDRO ◽  
J. L. G. SANTANDER ◽  
P. FERNÁNDEZ DE CÓRDOBA
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Ricci Flow ◽  
Mechanical Model ◽  
Quantum Dynamics ◽  
Deterministic Model ◽  
Quantum Mechanical ◽  
Deterministic System ◽  
Canonical Transformations ◽  
The Given

It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantization, the given quantum dynamics. For a quantum mechanics with a complex d-dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space ℂℙd-1 of quantum states. Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and let P denote the projection from the Hopf bundle onto its base ℂℙd-1. Then the underlying deterministic model we propose here is the Lie group SU(d), acted on by the operation PR. Finally we comment on some possible consequences that our model may have on a quantum theory of gravity.

scholarly journals Emergent quantum mechanics as a thermal ensemble

2014 ◽  
Vol 11 (08) ◽  
pp. 1450068 ◽  
Author(s):  
P. Fernández De Córdoba ◽  
J. M. Isidro ◽  
Milton H. Perea
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Thermal Fluctuations ◽  
Irreversible Processes ◽  
Quantum Mechanical ◽  
Transformation Theory ◽  
Time Irreversibility ◽  
Quantum Mechanical Systems ◽  
Emergent Quantum Mechanics

It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool toward this goal, we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.

Modelling Flexible Protein-Ligand Binding in p38α MAP Kinase using the QUBE Force Field

2019 ◽  
Author(s):  
Joshua Horton ◽  
Alice Allen ◽  
Daniel Cole
Keyword(s):  
Quantum Mechanics ◽  
Force Field ◽  
Map Kinase ◽  
Binding Free Energy ◽  
Quantum Mechanical ◽  
Enhanced Sampling ◽  
Relative Binding ◽  
Stringent Test ◽  
Flexible Protein ◽  
P38α Map Kinase

<div><div><div><p>The quantum mechanical bespoke (QUBE) force field is used to retrospectively calculate the relative binding free energy of a series of 17 flexible inhibitors of p38α MAP kinase. The size and flexibility of the chosen molecules represent a stringent test of the derivation of force field parameters from quantum mechanics, and enhanced sampling is required to reduce the dependence of the results on the starting structure. Competitive accuracy with a widely-used biological force field is achieved, indicating that quantum mechanics derived force fields are approaching the accuracy required to provide guidance in prospective drug discovery campaigns.</p></div></div></div>

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

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