scholarly journals EXACT SOLUTION AT INTEGRABLE COUPLING OF A MODEL FOR THE JOSEPHSON EFFECT BETWEEN SMALL METALLIC GRAINS

2002 ◽  
Vol 16 (23) ◽  
pp. 3429-3438 ◽  
Author(s):  
JON LINKS ◽  
HUAN-QIANG ZHOU ◽  
ROSS H. MCKENZIE ◽  
MARK D. GOULD
Keyword(s):  
Josephson Effect ◽  
Form Factors ◽  
Cooper Pairs ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Pair Tunneling ◽  
Scalar Products ◽  
Metallic Grains ◽  
Integrable Coupling ◽  
Small Metallic Grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

scholarly journals Spread of Entanglement in Non-Relativistic Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-27
Author(s):  
Sagar F. Lokhande
Keyword(s):  
Broad Class ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Instantaneous Power ◽  
Holographic Entanglement Entropy ◽  
Quantum Quenches ◽  
Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

scholarly journals The conformal anomaly action to fourth order (4T) in $$d=4$$ in momentum space

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio ◽  
Dimosthenis Theofilopoulos
Keyword(s):  
Momentum Space ◽  
Form Factors ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Independent Form ◽  
Stress Energy ◽  
Complete Determination ◽  
Non Local

AbstractWe elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $$R\square ^{-1}$$ R □ - 1 interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

Intrinsic Josephson effect and single Cooper pair tunneling

2000 ◽  
Vol 335 (1-4) ◽  
pp. 219-225 ◽  
Author(s):  
Tsutomu Yamashita ◽  
Sang-Jae Kim ◽  
Yuri Latyshev ◽  
Kensuke Nakajima
Keyword(s):  
Josephson Effect ◽  
Cooper Pair ◽  
Pair Tunneling ◽  
Cooper Pair Tunneling

JOSEPHSON π-STATE DUE TO SPIN-ACTIVE JUNCTION INTERFACE

2007 ◽  
Vol 21 (18n19) ◽  
pp. 3395-3397
Author(s):  
YASUHIRO ASANO ◽  
YUKI SAWA ◽  
YUKIO TANAKA
Keyword(s):  
Recent Experiment ◽  
Josephson Effect ◽  
Cooper Pairs ◽  
Half Metal ◽  
Spin Flip ◽  
Π State

Motivated by a recent experiment [R. S. Keizer, et. al., Nature 439, 825 (2006)], we study the Josephson effect in superconductor/diffusive half metal/superconductor junctions. The Josephson π-state is more stable than the 0-junction when the spin-flip scattering at the junction interface opens the Josephson channel of the odd-frequency Cooper pairs.

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