There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Advances in physics

Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons). The critical temperature of transition, energy, heat capacity and the transition heat of TI-bipolaron gas are calculated. The results obtained are used to explain experiments on high-temperature superconductors.

/pdf/superconducting-properties-of-3d-low-density-ti-bipolaron-b7gxdixia7.pdf

Superconducting properties of 3D low-density TI-bipolaron gas

Large-radius translation invariant (TI) bipolarons are considered in a one-dimensional Holstein molecular chain. Criteria of their stability are obtained. The energy of a translation invariant bipolaron is shown to be lower than that of a bipolaron with broken symmetry. The results obtained are applied to the problem of superconductivity in 1D-systems. It is shown that TI-bipolaron mechanism of Bose-Einstein condensation can support superconductivity even for infinite chain.

/pdf/a-translation-invariant-bipolaron-in-the-holstein-model-and-41rhnrj4vx.pdf

A translation invariant bipolaron in the Holstein model and superconductivity.

The properties of a Bose gas of translation-invariant (TI) bipolarons analogous to Cooper pairs are considered. As in the BCS theory, the description of a TI-bipolaron gas is based on the electron-phonon interaction and Froehlich Hamiltonian. As distinct from the BCS theory, when the correlation length greatly exceeds the mean distance between the pairs, here we deal with the opposite case when the correlation length is much less than the distance between the pairs. We calculate the critical temperature of the transition of a TI-bipolaron Bose-gas into the superconducting state, its energy, heat capacity and heat of the transition. The results obtained are used to explain the experiments on high-temperature superconductors. Possible ways of raising the critical temperature of high-temperature superconductors are discussed.

Superconducting properties of a nonideal bipolaron gas

The charge transfer in a Holstein molecular chain placed in a uniform electric field has been numerically simulated. It has been shown that for given parameters of the chain, a charge placed in a constant electric field may uniformly travel very large distances (several hundred thousand sites). The charge may move with a constant velocity if the field strength is low. With an increase in the field strength, the charge starts oscillating (Bloch oscillations). Good agreement has been shown between the theoretical and numerical field dependences of the charge constant velocity.

Simulation of the Stationary and Nonstationary Charge Transfer Conditions in a Uniform Holstein Chain Placed in Constant Electric Field

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Frohlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

https://www.mdpi.com/2410-3896/5/2/30/pdf

Victor Dmitrievich Lakhno

Papers

Superconducting properties of 3D low-density TI-bipolaron gas

A translation invariant bipolaron in the Holstein model and superconductivity.

Superconducting properties of a nonideal bipolaron gas

Simulation of the Stationary and Nonstationary Charge Transfer Conditions in a Uniform Holstein Chain Placed in Constant Electric Field

Translational-Invariant Bipolarons and Superconductivity