ON THE SHORT-TIME BEHAVIOR OF QUANTUM MECHANICAL SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3103-3111 ◽  
Author(s):  
HIROMICHI NAKAZATO ◽  
SAVERIO PASCAZIO

The conditions that yield deviations from a purely exponential behavior of a quantum mechanical system at short times are analyzed with special emphasis on the boundedness of the Hamiltonian. A few practical examples are considered. The problem of dissipation in quantum mechanics and quantum field theory is also briefly discussed.

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Mabrouk Benhamou

Diffusion-reaction phenomena are generally described by parabolic differential equations (PDEs), and I am interested in those possessing solutions that fail at large time. A sophisticated method to study the large-time behavior is the Renormalization Group usually encountered in Particles-Physics and Critical Phenomena. In this paper, I review the application of such an approach. In particular, attention is paid to Quantum Field Theory techniques used for the extraction of the asymptotic solutions to PDEs. Finally, I extend discussion to the fractional-time PDEs and with noise.


2021 ◽  
Author(s):  
Wim Vegt

Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.


2021 ◽  
Author(s):  
Wim Vegt

Isaac Newton and Albert Einstein lived in fundamentally different time frames. An interesting question would be: “Who would win the fundamental discussion about the interaction between gravity and light”? Einstein or Newton? Einstein with the fundamental concept of a “curved space-time continuum” within a gravitational field. Or Newton with the fundamental “3rd law of equilibrium between the forces (force-densities)”. It is still the question who was right? Einstein or Newton? Einstein assumes a deformation of the space-time continuum because of a gravitational field. But in general a deformation of any medium will be caused by the change of the energy density within the medium. Like the speed of sound will increase/ decrease when we change the air pressure. However, the speed of sound (which became higher or lower) will still be the same in any direction. The change of the speed of sound will be omni-directional.A gravitational field contains a gravitational energy-density. For that reason the change in the speed of light will be omni-directional within a gravitational field (with a omni-directional gravitational energy density). Einstein however assumes a one-directional change in the speed of light, (only in the direction of the gravitational field). When the change of the speed of light was omni-directional, a beam of light would never be deflected by a gravitational field which is in contradiction with what we measure. Only the absolute value of the speed of light would change omni-directional.The theory of Newton however results in the theory of a 2-directional inertia of photons. The inertia of photons equals zero only in the direction of propagation. Perpendicular to the direction of propagation the mass density of photons is according Einstein’s E = m c^2).The inertia of photons in the direction of propagation will not change within a gravitational field. Gravity can only interact with mass (inertia). Because the mass of the photons in the direction of propagation equals zero, there will ne no interaction with the gravitational field and the photon in the direction of propagation. The speed of light in the direction of propagation will remain unaltered. But according Newton, the photon will have inertia (mass) in the directions perpendicular to the direction of propagation and for that reason the photon will interact with the gravitational field and the photon will be deflected, only in the direction of the gravitational field.And that leads to the consequence that photons will be deflected within a gravitational field when the direction of the gravitational field is perpendicular to the direction of propagation of the photons.To find fundamental mathematical evidence for this concept, we have to make use of Quantum Light Theory. Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.


2021 ◽  
Author(s):  
Wim Vegt

The fundamental principle in General Relativity is to combine the inertia of mass and the relationship with the gravity force acting on this mass. In this article a new concept in General Relativity will be introduced. The concept of the “Paradox in a Curved Space-Time Continuum”. The “Paradox in a Curved Space-Time Continuum” has been based on the fundamental question: Does light follow a curved path within a gravitational field because a gravitational field causes a “Curved Space Time Continuum” or does a curved path of a beam of light generate a Gravitational Field. Differently formulated: Is Gravity a second order effect of a curved Electromagnetic field?To answer this question a new theory will be introduced. The “Quantum Light Theory” which is a specialization of “Quantum Field Theory”.Quantum Light Theory (QLT) is the new development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. In which gravity is the second order effect of the fundamental Electromagnetic Field. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.


1994 ◽  
Vol 09 (23) ◽  
pp. 2167-2178 ◽  
Author(s):  
D.G.C. MCKEON ◽  
T.N. SHERRY

It has been shown how evaluation of matrix elements of the form <x| exp −iHt|y> using the quantum mechanical path-integral allows one to determine radiative corrections in quantum field theory without encountering loop momentum integrals. In this paper we show how this technique can be applied when there is a constant background magnetic field contributing to the “Hamiltonian” H.


2008 ◽  
Vol 23 (02) ◽  
pp. 299-308 ◽  
Author(s):  
MARCO FRASCA

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher-order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.


2010 ◽  
Vol 25 (22) ◽  
pp. 4179-4194 ◽  
Author(s):  
MASSIMO BLASONE ◽  
ANTONIO CAPOLUPO ◽  
CHUENG-RYONG JI ◽  
GIUSEPPE VITIELLO

In the context of quantum field theory (QFT), we compute the amplitudes of weak interaction processes such as W+ →e+ + νe and W+ →e+ + νμ by using different representations of flavor states for mixed neutrinos. Analyzing the short time limit of the above amplitudes, we find that the neutrino states defined in QFT as eigenstates of the flavor charges lead to results consistent with lepton charge conservation. On the contrary, the Pontecorvo flavor states produce a violation of lepton charge in the vertex, which is in contrast with what expected at tree level in the Standard Model.


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