scholarly journals Quantum and semiclassical Cooper–pair tunneling in finite systems

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
M. Kleber
Keyword(s):  
Semiclassical Limit ◽  
Finite Size ◽  
Tunneling Current ◽  
Analytic Solutions ◽  
Cooper Pairs ◽  
Chemical Potentials ◽  
Weakly Coupled ◽  
Pair Tunneling ◽  
Starting Point ◽  
Tunneling Dynamics

AbstractWe derive analytic solutions for the tunneling dynamics of two weakly coupled finite BCS–condensates. Pairing interaction between the finite–size condensates is taken into account. Using particle–number dependent chemical potentials the time–dependent transfer of Cooper pairs is obtained from a phenomenological calculation. The results of this theory are compared to a microscopic calculation within the quasispin formulation in its semiclassical limit. In both cases the tunneling current can be mapped onto the motion of a simple pendulum: The results are analogous to the Josephson current between two superconductors and can be used as a starting point to include quantum fluctuations and Josephson radiation.

scholarly journals Finite-size effects in metallic superlattice systems

1995 ◽  
Vol 73 (9-10) ◽  
pp. 545-553
Author(s):  
J. Chen ◽  
R. Kobes ◽  
J. Wang
Keyword(s):  
Critical Temperature ◽  
Simple Model ◽  
Proximity Effect ◽  
Size Effects ◽  
Finite Size ◽  
Cooper Pairs ◽  
Superconducting Layer ◽  
Finite Size Effects ◽  
Realistic Form ◽  
Pair Amplitude

Clean metallic superlattice systems composed of alternating layers of superconducting and normal materials are considered, particularly aspects of the proximity effect as it affects the critical temperature. A simple model is used to address the question of when a finite–sized system theoretically approximates well a true infinite superlattice. The methods used in the analysis afford some tests of the approximation used that the pair amplitude of the Cooper pairs is constant over a superconducting region. We also use these methods to construct a model of a single superconducting layer which intends to incorporate a more realistic form of the pair amplitude than a simple constant.

Influence of Finite Size Effects on the Fulde-Ferrell-Larkin-Ovchinnikov State

2017 ◽  
Vol 21 (3) ◽  
pp. 748-762 ◽  
Author(s):  
Andrzej Ptok ◽  
Dawid Crivelli
Keyword(s):  
Fermi Surface ◽  
Size Effects ◽  
Cooper Pair ◽  
Finite Size ◽  
Superconducting Phase ◽  
Cooper Pairs ◽  
Fflo State ◽  
Finite Size Effects ◽  
Infinite Systems ◽  
Nano Size

AbstractThe Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is the superconducting phase for which the Cooper pairs have a non-zero total momentum, depending on the splitting of the Fermi surface sheets for electrons with opposite spin. In infinite systems the momentum is a continuous function of the temperature. In this paper, we have shown how the finite size of the system, through the discretized geometry of the Fermi surface, affects the physical properties of the FFLO state by introducing discontinuities in the Cooper pair momentum. Our calculation in an isotropic system show that the superconducting state with two opposite Cooper pair momenta is more stable than state with one momentum also in nano-size systems, where finite size effects play a crucial role.

scholarly journals Quantum tunneling theory of Cooper pairs as bosonic particles

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Edgar J. Patiño ◽  
Daniel Lozano-Gómez
Keyword(s):  
Quantum Tunneling ◽  
Alternative Explanation ◽  
Tunnel Junctions ◽  
Tunneling Current ◽  
Phenomenological Theory ◽  
Low Energy ◽  
Cooper Pairs ◽  
Zero Bias ◽  
Conductance Peak ◽  
Zero Bias Conductance

AbstractWe propose a simple phenomenological theory for quantum tunneling of Cooper pairs, in superconductor/insulator/superconductor tunnel junctions, for a regime where the system can be modeled as bosonic particles. Indeed, provided there is an absence of quasiparticle excitations (fermions), our model reveals a rapid increase in tunneling current, around zero bias voltage, which rapidly saturates. This manifests as a zero bias conductance peak that strongly depends on the superconductors temperature in a non-monotonic way. This low energy tunneling of Cooper pairs could serve as an alternative explanation for a number of tunneling experiments where zero bias conductance peak has been observed.

scholarly journals Effect of Plastic Anisotropy on the Collapse of a Hollow Disk under Thermal and Mechanical Loading

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 909
Author(s):  
Elena Lyamina
Keyword(s):  
Plastic Anisotropy ◽  
Plastic Region ◽  
Finite Size ◽  
Analytic Solutions ◽  
Outer Radius ◽  
The Other ◽  
Plastic Collapse ◽  
Essential Difference ◽  
Plastic Yielding ◽  
Inner Radius

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and preliminary design of such structures. The present paper is devoted to describing the plastic collapse of a thin orthotropic hollow disk inserted into a rigid container. The disk is subject to a uniform temperature field and a uniform pressure is applied over its inner radius. The condition of axial symmetry in conjunction with the assumption of plane stress, permits an exact analytic solution. Two plastic collapse mechanisms exist. One of these mechanisms requires that the entire disk is plastic. According to the other mechanism, plastic deformation localizes at the inner radius of the disk. Additionally, two special solutions are possible. One of these solutions predicts that the entire disk becomes plastic at the initiation of plastic yielding (i.e., plastic yielding simultaneously initiates in the entire disk). The other special solution predicts that the plastic localization occurs at the inner radius of the disk with no plastic region of finite size. An essential difference between the orthotropic and isotropic disks is that plastic yielding might initiate at the outer radius of the orthotropic disk.

scholarly journals Mathematical model for tissue stresses in growing plant cells and organs

2011 ◽  
Vol 78 (1) ◽  
pp. 19-23
Author(s):  
Mariusz Pietruszka ◽  
Sylwia Lewicka
Keyword(s):  
Mathematical Model ◽  
Equilibrium Equation ◽  
Turgor Pressure ◽  
Plant Cells ◽  
Analytic Solutions ◽  
Simple Mathematical Model ◽  
Single Plant ◽  
Starting Point ◽  
Good Starting Point ◽  
Tissue Stresses

In this study we propose a simple mathematical model based on the equilibrium equation for the materials deformed elastically. Owing to the turgor pressure of the cells, the peripheral walls of the outer tissue are under tension, while the extensible inner tissue is under compression. This well known properties of growing multicellular plant organs can be derived from the equation for equilibrium. The analytic solutions may serve as a good starting point for modeling the growth of a single plant cell or an organ.

scholarly journals Analytic Solutions of the Rotating and Stratified Hydrodynamical Equations

2021 ◽  
pp. 14-26
Author(s):  
Imre F. Barna ◽  
L. Mátyás
Keyword(s):  
Euler Equations ◽  
Power Law ◽  
Mathematical Structure ◽  
Analytic Solutions ◽  
Velocity Fields ◽  
Pressure Fields ◽  
Starting Point ◽  
Self Similar ◽  
Explosive Properties ◽  
Scientific Fields

In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating,  just stratified Euler equations, comparing with each other and with the normal Euler equations with  the self-similar Ansatz. The motivation of our study is the following the presented rotating stratified  fluid equations can be interpreted as a well-established starting point of various more complex and  more realistic meteorologic, oceanographic or geographic models. We present analytic solutions  for all four models for density, pressure and velocity fields, most of them are some kind of power-law  type of functions. In general the presented solutions have a rich mathematical structure. Some  solutions show nonphysical explosive properties others, however are physically acceptable and  have finite numerical values with power law decays. For a better transparency we present some figs  for the most complicated velocity and pressure fields. To our knowledge there are no such analytic  results available in the literature till today. Our results may attract attention in various scientific fields.   

scholarly journals A Geometrical Analysis of Global Stability in Trained Feedback Networks

2019 ◽  
Vol 31 (6) ◽  
pp. 1139-1182 ◽  
Author(s):  
Francesca Mastrogiuseppe ◽  
Srdjan Ostojic
Keyword(s):  
Global Stability ◽  
Dimensional Space ◽  
Mean Field Theory ◽  
Mean Field ◽  
Finite Size ◽  
Analytical Description ◽  
Global Dynamics ◽  
Stability Properties ◽  
Starting Point ◽  
Feedback Networks

Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has been achieved, a full understanding of trained recurrent networks is still lacking. Specifically, the mechanisms that allow computations to emerge from the underlying recurrent dynamics are largely unknown. Here we focus on a simple yet underexplored computational setup: a feedback architecture trained to associate a stationary output to a stationary input. As a starting point, we derive an approximate analytical description of global dynamics in trained networks, which assumes uncorrelated connectivity weights in the feedback and in the random bulk. The resulting mean-field theory suggests that the task admits several classes of solutions, which imply different stability properties. Different classes are characterized in terms of the geometrical arrangement of the readout with respect to the input vectors, defined in the high-dimensional space spanned by the network population. We find that such an approximate theoretical approach can be used to understand how standard training techniques implement the input-output task in finite-size feedback networks. In particular, our simplified description captures the local and the global stability properties of the target solution, and thus predicts training performance.

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