SQUID Magnetometers, Josephson Junctions, Confinement and BCS Theory of Superconductivity

2020 ◽  
Author(s):  
Navin Khaneja
Keyword(s):  
Magnetic Flux ◽  
Materials Science ◽  
Wave Packets ◽  
Finite Size ◽  
Transition Amplitude ◽  
Local Potential ◽  
Bcs Theory ◽  
Finite Width ◽  
S Wave ◽  
Theory Of Superconductivity

A superconducting quantum interference device (SQUID) is the most sensitive magnetic flux sensor currently known. The SQUID can be seen as a flux to voltage converter, and it can generally be used to sense any quantity that can be transduced into a magnetic flux, such as electrical current, voltage, position, etc. The extreme sensitivity of the SQUID is utilized in many different fields of applications, including biomagnetism, materials science, metrology, astronomy and geophysics. The heart of a squid magnetometer is a tunnel junction between two superconductors called a Josephson junction. Understanding the work of these devices rests fundamentally on the BCS theory of superconductivity. In this chapter, we introduce the notion of local potential and confinement in superconductivity. We show how BCS ground state is formed from interaction of wave packets confined to these local potential wells. The starting point of the BCS theory of superconductivity is a phonon-mediated second-order term that describes scattering of electron pair at Fermi surface with momentum k i , − k i and energy 2 ℏ ω i to k j , − k j with energy 2 ℏ ω j . The transition amplitude is M = − d 2 ω d ω i − ω j 2 − ω d 2 , where d is the phonon scattering rate and ω d is the Debye frequency. However, in the presence of offset ω i − ω j , there is also a present transition between states k i , − k i and k j , − k i of sizable amplitude much larger than M . How are we justified in neglecting this term and only retaining M ? In this chapter, we show all this is justified if we consider phonon-mediated transition between wave packets of finite width instead of electron waves. These wave packets are in their local potentials and interact with other wave packets in the same well to form a local BCS state we also call BCS molecule. Finally, we apply the formalism of superconductivity in finite size wave packets to high Tc in cuprates. The copper electrons in narrow d-band live as packets to minimize the repulsion energy. The phonon-mediated coupling between wave packets (of width Debye energy) is proportional to the number of k-states in a packet, which becomes large in narrow d-band (10 times s-band); hence, d-wave Tc is larger (10 times s-wave). At increased doping, packet size increases beyond the Debye energy, and phonon-mediated coupling develops a repulsive part, destroying superconductivity at large doping levels.

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

Corrections for surface X-ray diffraction measurements using theZ-axis geometry: finite size effects in direct and reciprocal space

2000 ◽  
Vol 33 (4) ◽  
pp. 1006-1018 ◽  
Author(s):  
O. Robach ◽  
Y. Garreau ◽  
K. Aïd ◽  
M. B. Véron-Jolliot
Keyword(s):  
Correction Factor ◽  
Finite Size ◽  
Grazing Incidence ◽  
Sample Surface ◽  
Finite Width ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plane Shape ◽  
Sample Approximation ◽  
Effective Part

X-ray diffraction data have to be corrected by geometrical correction factors prior to any quantitative analysis. Here the case of grazing incidence X-ray diffraction measurements is considered, including the case of high exit angles. First, an approach taking into account the evolution of the diffracting area during an ω scan is presented. From the calculation of the effective part of the sample surface that participates in the diffraction phenomena at each step of the scan, a more accurate correction factor than those commonly used is derived and the evolution of the line shape along a zero-width rod is explained. Secondly, the case of finite-width rods, under the point-like sample approximation, is considered: the influence of the partial integration, as a result of the detector in-plane acceptance, of a rod with an anisotropic in-plane shape, is studied and leads to an analytical expression for the corresponding correction factor. Finally, a full numerical simulation is presented, which provides an alternative method for correcting the experimental intensities and shows in which conditions the previous formulae are no longer valid.

N-quantum approach to the BCS theory of superconductivity

1994 ◽  
Vol 72 (9-10) ◽  
pp. 574-577 ◽  
Author(s):  
O. W. Greenberg
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Bcs Theory ◽  
Zero Temperature ◽  
General Applicability ◽  
Finite Temperature Field Theory ◽  
Gap Equation ◽  
Quantum Approach ◽  
Quantized Field ◽  
Theory Of Superconductivity

A method of general applicability to the solution of second-quantized field theories at finite temperature is illustrated using the BCS (Bardeen–Cooper–Schrieffer) model of superconductivity. Finite-temperature field theory is treated using the thermo field-theory formalism of Umezawa and collaborators. The solution of the field theory uses an expansion in thermal modes analogous to the Haag expansion in asymptotic fields used in the N-quantum approximation at zero temperature. The lowest approximation gives the usual gap equation.

Energy Spectrum and Persistent Currents in Finite-Width Mesoscopic Ring with Radial Potential Barrier Threading a Magnetic Flux Through its Hole

1998 ◽  
Vol 12 (06) ◽  
pp. 663-672
Author(s):  
Ben-Yuan Gu ◽  
Wei-Dong Sheng ◽  
Jian Wang
Keyword(s):  
Energy Spectrum ◽  
Magnetic Flux ◽  
Potential Barrier ◽  
Coupling Effect ◽  
Finite Width ◽  
Persistent Currents ◽  
Tunneling Barrier ◽  
Radial Potential ◽  
Mesoscopic Ring

The energy spectrum and the persistent currents are calculated for a finite-width mesoscopic annulus with radial potential barrier, threading a magnetic flux through the hole of the ring. Owing to the presence of tunneling barrier, the coupling effect leads to the splitting of each radial energy subband of individual concentrical rings into two one. Thus, total currents and currents carried by single high-lying eigenstate as a function of magnetic flux exhibit complicated patterns. However, periodicity and antisymmetry of current curves in the flux still preserve.

Zero-temperature equation-of-motion of electron pair in the BCS theory of superconductivity

1996 ◽  
Vol 74 (6) ◽  
pp. 1106-1115
Author(s):  
Akitomo Tachibana
Keyword(s):  
Hilbert Space ◽  
Density Functional ◽  
Electron Pair ◽  
Equation Of Motion ◽  
Real Space ◽  
Bcs Theory ◽  
Zero Temperature ◽  
Functional Theory ◽  
Theory Of Superconductivity ◽  
Pair Function

By projecting the BCS ground state of superconducting electron condensate on the N-electron Hilbert space, a real-space equation-of-motion is obtained for the electron pair function [Formula: see text] at absolute zero temperature (T = 0):[Formula: see text]where ρN−2 denotes electron density of the (N – 2)-electron condensate given as[Formula: see text]Since the exchange-correlation potential is given as an explicit functional of electron density, this equation represents the fundamental working equation for the new density functional theory of superconductivity. The 2nd-order density matrix ΓN(1, 2|1′, 2′) projected on the N-electron Hilbert space satisfies[Formula: see text]so that asymptotically[Formula: see text]where [Formula: see text] denotes the center-of-mass coordinate of electrons e1and e2; this is considered the ODLRO (off-diagonal long-range order) at T = 0 projected on the N-electron Hilbert space. A new attractive potential analysis for the two-electron scattering problem (A. Tachibana, Bull. Chem. Soc. Jpn. 66, 3319 (1993); Int. J. Quantum Chem. 49, 625 (1994)) is straightforwardly applicable to the present equation-of-motion, and we can also plug in the vibronic interaction for the enhancement of the attractive force. Our approach is purely mathematical and basic, restricted merely at T = 0, but proves to serve as a real-space analysis of the pair function itself. Key words: equation-of-motion of electron pair, BCS theory, superconductivity, electron pair function, density functional theory.

scholarly journals Raman Processes in the Helium Atom in Intense Fields

1975 ◽  
Vol 28 (1) ◽  
pp. 35
Author(s):  
RK Thareja ◽  
Man Mohan ◽  
V Nayak ◽  
SN Haque
Keyword(s):  
Helium Atom ◽  
General Expression ◽  
High Intensity ◽  
Transition Amplitude ◽  
Higher Order ◽  
Nonlinear Behaviour ◽  
S Wave ◽  
Intensity Parameter ◽  
Intense Fields ◽  
Hydrogenic Model

Using the hydrogenic model for the helium atom, the amplitude of transition from states He(ls) to He(ls, nl) by absorption of N photons of an intense field together with the emission of one Raman photon is evaluated. From the general expression for the transition amplitude, the particular case of transition from He(ls) to He(ls, 2p) is considered. The 'reduced' transition amplitude is plotted against the number of photons N involved and against the intensity parameter y st;parately. It is found that the s wave contributes maximaly to the transition amplitude. An important feature of the calculations is the appearance of nonlinear behaviour at high intensity. The dominance of higher order processes over lower ones at high intensity is also found.

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