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Shape Waves
Shape waves are excitations propagating along Josephson vortices or fluxons. In the case of two-dimensional Josephson junctions (thick long Josephson junctions with an extra dimension) described by the 2D sine-Gordon equation, shape waves are distortions of a Josephson vortex line of an arbitrary profile. Shape waves have remarkable properties exhibiting Lorentz contraction and time dilation similar to that in special relativity. Position of the shape wave excitation on a Josephson vortex In superconductivity, a Josephson vortex (after Brian David Josephson, Brian Josephson from Cambridge University) is a quantum vortex of supercurrents in a long Josephson junction, Josephson junction (see Josephson effect). The supercurrents circu ... acts like a “minute-hand” showing the time in the rest-frame associated with the vortex. At some conditions, a moving vortex with the shape excitation can have less energy than the same vortex without it. References * Waves {{phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josephson Vortices
In superconductivity, a Josephson vortex (after Brian Josephson from Cambridge University) is a quantum vortex of supercurrents in a Josephson junction (see Josephson effect). The supercurrents circulate around the vortex center which is situated inside the Josephson barrier, unlike Abrikosov vortices in type-II superconductors, which are located in the superconducting condensate. Abrikosov vortices (after Alexei Abrikosov) in superconductors are characterized by normal cores where the superconducting condensate is destroyed on a scale of the superconducting coherence length ''ξ'' (typically 5-100 nm) . The cores of Josephson vortices are more complex and depend on the physical nature of the barrier. In Superconductor-Normal Metal-Superconductor (SNS) Josephson junctions there exist measurable superconducting correlations induced in the N-barrier by proximity effect from the two neighbouring superconducting electrodes. Similarly to Abrikosov vortices in superconductors, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluxons
In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings. Superconductivity In the context of superconductivity, in type II superconductors fluxons (also known as Abrikosov vortices) can form when the applied field lies between B_ and B_. The fluxon is a small whisker of normal phase surrounded by superconducting phase, and Supercurrents circulate around the normal core. The magnetic field through such a whisker and its neighborhood, which has size of the order of London penetration depth \lambda_L (~100 nm), is quantized because of the phase properties of the magnetic vector potential in quantum electrodynamics, see magnetic flux quantum for details. In the context of long Superconductor-Insulator-Superconductor Josephson tunnel junctions, a fluxon (aka Josephson vortex) is made of circulating supercurrents and has ''no'' normal core in the tunneling barrier. Supercurrents circulate just around the mathematical center of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josephson Junctions
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. :Also in It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements. The Josephson effect produces a current, known as a supercurrent, that flows continuously without any voltage applied, across a device known as a Josephson junction (JJ). These consist of two or more superconductors coupled by a weak link. The weak link can be a thin insulating barrier (known as a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Long Josephson Junction
In superconductivity, a long Josephson junction (LJJ) is a Josephson junction which has one or more dimensions longer than the Josephson penetration depth \lambda_J. This definition is not strict. In terms of underlying model a ''short Josephson junction'' is characterized by the Josephson phase \phi(t), which is only a function of time, but not of coordinates i.e. the Josephson junction is assumed to be point-like in space. In contrast, in a long Josephson junction the Josephson phase can be a function of one or two spatial coordinates, i.e., \phi(x,t) or \phi(x,y,t). Simple model: the sine-Gordon equation The simplest and the most frequently used model which describes the dynamics of the Josephson phase \phi in LJJ is the so-called perturbed sine-Gordon equation. For the case of 1D LJJ it looks like: where subscripts x and t denote partial derivatives with respect to x and t, \lambda_J is the Josephson penetration depth, \omega_p is the Josephson plasma frequency, \omega_c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine-Gordon Equation
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function \varphi dependent on two variables typically denoted x and t, involving the wave operator and the sine of \varphi. It was originally introduced by in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of constant Gaussian curvature −1 in 3-dimensional space. The equation was rediscovered by in their study of crystal dislocations known as the Frenkel–Kontorova model. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions, and is an example of an integrable PDE. Among well-known integrable PDEs, the sine-Gordon equation is the only ''relativistic'' system due to its Lorentz invariance. Realizations of the sine-Gordon equation Differential geometry This is the first derivation of the equation, by Bour (1862). There are two equivalent forms of the sine-Gordon equation. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josephson Vortex
In superconductivity, a Josephson vortex (after Brian David Josephson, Brian Josephson from Cambridge University) is a quantum vortex of supercurrents in a long Josephson junction, Josephson junction (see Josephson effect). The supercurrents circulate around the vortex center which is situated inside the Josephson barrier, unlike Abrikosov vortex, Abrikosov vortices in type-II superconductors, which are located in the superconducting condensate. Abrikosov vortex, Abrikosov vortices (after Alexei Alexeyevich Abrikosov, Alexei Abrikosov) in superconductors are characterized by normal cores where the superconducting condensate is destroyed on a scale of the superconducting coherence length ''ξ'' (typically 5-100 nm) . The cores of Josephson vortices are more complex and depend on the physical nature of the barrier. In Superconductor-Normal Metal-Superconductor (SNS) long Josephson junction, Josephson junctions there exist measurable superconducting correlations induced in the N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Contraction
Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboardist * Lorentz Dietrichson (1834–1917), Norwegian poet and historian of art and literature * Lorentz Eichstadt (1596–1660), German mathematician and astronomer * Lorentz Harboe Ree (1888–1962), Norwegian architect * Lorentz Lange (1783–1860), Norwegian judge and politician * Lorentz Reige (born 1990), Swedish dancer * Lorentz Reitan (born 1946), Norwegian musicologist Mononym * Lorentz (rapper), real name Lorentz Alexander, Swedish singer and rapper Surname * Dominique Lorentz, French investigative journalist who has written books on nuclear proliferation * Friedrich Lorentz, author of works on the Pomeranian language * Geertruida de Haas, née Lorentz, Dutch physicist * Hendrik Antoon Lorentz (1853–1928), Dutch physicis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Dilation
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity. The dilation compares "wristwatch" clock readings between events measured in different inertial frames and is not observed by visual comparison of clocks across moving frames. These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo. Invisibility Time dilation is a relationship between clock readings. Visually observed clock readings involve delays due to the propagation speed of light from the clock to the observer. Thus there is no direct way to observe time dilation. As an example of time dilation, two expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Electrodynamics of Moving Bodies", the theory is presented as being based on just Postulates of special relativity, two postulates: # The laws of physics are Invariant (physics), invariant (identical) in all Inertial frame of reference, inertial frames of reference (that is, Frame of reference, frames of reference with no acceleration). This is known as the principle of relativity. # The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance. The first postulate was first formulated by Galileo Galilei (see ''Galilean invariance''). Background Special relativity builds upon important physics ide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
