The Quantum-Field Approach to Superconductivity Theory

Kruchinin, S. P.

doi:10.1166/rits.2016.1053

Cited by 2 publications

(2 citation statements)

References 32 publications

(32 reference statements)

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“…Certainly, the fact that the expectation value of the energy density associated with a quantum free scalar field measured on an inertial world line of the Minkowski space-time may be negative becomes relevant since this fact has important implications on a number of aspects of quantum physics, aspects related to quantum field theory being perhaps the most significant ones [5][6][7][8][9][10][11][12][13][14][15]. By theorem 1, we have deduced the minimal value taken on by ( ) p u ; this is a useful condition to be fulfilled by the function ( ) p u whose relevance is clearly manifest.…”

Section: Discussionmentioning

confidence: 99%

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Grado-Caffaro¹

2017

NHMP

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Abstract. After presenting a lemma, two theorems on negative energy density associated with a quantum free scalar field are established. The first theorem provides a lower bound for a non-negative weight function whose existence is guaranteed by the lemma. The above energy density is evaluated over an inertial world line of the Minkowski space-time. The second theorem provides an upper bound for the averaged (with respect to the sampling function) absolute expectation value of the negative energy-density function. In particular, a complex-valued sampling function is introduced by the first time so a more generalized formulation is proposed. IntroductionIn quantum field theory, one can find very interesting examples on negative energy density (see, for instance, ref.[1]). Referring to the general context of quantum physics, there are cases in which energy density can be negative. In this respect, the Casimir effect (see, for example, ref.[1]) is certainly relevant: the quantum fluctuations of the electromagnetic field in the vacuum give rise to a macroscopic effect (Casimir effect) by which the electromagnetic-energy density is negative in the cavity formed by two conducting plates separated by a certain distance. One can think that, in principle, the energy density associated with a quantum field can be made arbitrarily negative at any point of the space-time by choosing a suitable state. Despite considering a classical field in which energy densities are positive in every point of the space-time, the renormalized energy density of the field quantized from the above classical field can be zero and can take either strictly positive or strictly negative values (note that the above density must be continuous). In principle, the renormalized energy density in question may even be made arbitrarily negative at a given point of the space-time. As a matter of fact, arbitrarily negative expectation values of the energy density can be measured after quantization even though the spatially integrated density holds non-negative. The aim of the present paper lies on proving two useful theorems about negative energy density of a free scalar field on an inertial world line of the Minkowski space-time. In this context, we may consider, for example, Dirac or Klein-Gordon fields. On the other hand, a key ingredient in the hypotheses of the above theorems is assuming realistically that the energy density of the aforementioned free scalar field cannot take on negative values arbitrarily. Really, negative energy density is constrained to certain conditions so that the negativeness of the density is not arbitrary; those conditions have been formulated currently by means of quantum inequalities. Before establishing the theorems in question, we will enunciate a lemma which certainly contributes enough to the clarification of the state of the art. In addition, a complex-valued sampling function will be introduced.

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Section: Discussionmentioning

confidence: 99%

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Grado-Caffaro¹

2017

NHMP

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“…In papers [9][10][11][12][13][14][15][16] it has been proposed a superlattice model of graphene on a support, for example, on hexagonal boron nitride. It has been shown that a Hamiltonian of the superlattice represents itself a Hamiltonian of monolayer graphene with corrections to pseudo-electric and pseudo-magnetic fields which strain the graphene monolayer.…”

Section: Electronic Properties Of Twisted Bilayer Graphenementioning

confidence: 99%

Electronic properties of twisted bilayer graphene in high-energy k ⋅p-Hamiltonian approximation

et al. 2020

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A model of twisted bilayer graphene has been offered on the base of developed quasi-relativistic approach with high energy [Formula: see text]-Hamiltonian. Monolayer-graphene twist is accounted as a perturbation of monolayer-graphene Hamiltonian in such a way that at a given point of the Brillouin zone there exists an external non-Abelian gauge field of another monolayer. Majorana-like resonances have been revealed in the band structure of model at a magic rotation angle [Formula: see text]. The simulations have also shown that a superlattice energy gap existing at a rotation angle [Formula: see text] vanishes at a rotation angle [Formula: see text].

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The Quantum-Field Approach to Superconductivity Theory

Cited by 2 publications

References 32 publications

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Electronic properties of twisted bilayer graphene in high-energy k ⋅p-Hamiltonian approximation

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