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... exponents which vary with x in a wide regime x ≥ xc [2, 3]. This marks the quantum Griffiths phase (GP) (see e.g. in [10]), characterized by a distribution of magnetic clusters with different fluctuation rates. This phase is distinctly different than in clean QPT, where universal critical exponents ...
... exponents which vary with x in a wide regime x ≥ xc [2, 3]. This marks the quantum Griffiths phase (GP) (see e.g. in [10]), characterized by a distribution of magnetic clusters with different fluctuation rates. This phase is distinctly different than in clean QPT, where universal critical exponents ...
Witten
... lution of this problem. In addition to the elementary fermions and their bound states, this model contains also kink states, associated with the spontaneous breaking of the discrete chiral symmetry. The kinks interpolate between the two possible vacuum states at spatial infinity, and a semiclassical ...
... lution of this problem. In addition to the elementary fermions and their bound states, this model contains also kink states, associated with the spontaneous breaking of the discrete chiral symmetry. The kinks interpolate between the two possible vacuum states at spatial infinity, and a semiclassical ...
Vacuum Energy and Effective Potentials
... Consequently, the zero-point energy of the δϕ field remains constant, but the zero-point energy of Φ depends on the M 2 and hence on the hϕi, so let’s calculate this energy and its ...
... Consequently, the zero-point energy of the δϕ field remains constant, but the zero-point energy of Φ depends on the M 2 and hence on the hϕi, so let’s calculate this energy and its ...
Gauge Field Theories Second Edition - Assets
... this chapter are not necessarily only the fields which describe the classical forces observed in Nature. 1.1 The action, equations of motion, symmetries and conservation laws Equations of motion All fundamental laws of physics can be understood inR terms of Ra mathematical construct: the action. An ...
... this chapter are not necessarily only the fields which describe the classical forces observed in Nature. 1.1 The action, equations of motion, symmetries and conservation laws Equations of motion All fundamental laws of physics can be understood inR terms of Ra mathematical construct: the action. An ...
Academia Sinica, Taipei, Taiwan, 06/2010, Yip Sungkit
... 4. The dual CFT (quiver SU(N) gauge theory) is known for some ƒ 5. By tuning ƒ we can reproduce different phase transitions ...
... 4. The dual CFT (quiver SU(N) gauge theory) is known for some ƒ 5. By tuning ƒ we can reproduce different phase transitions ...
Higgs - mechanism
... second order phase transition corresponds to critical surface in general space of couplings flow of couplings remains within critical surface once couplings are near critical surface at one scale, they remain in the vicinity of critical surface gauge hierarchy problem : explain why world is near cri ...
... second order phase transition corresponds to critical surface in general space of couplings flow of couplings remains within critical surface once couplings are near critical surface at one scale, they remain in the vicinity of critical surface gauge hierarchy problem : explain why world is near cri ...
Doctoral Programmes in Physics at IMSc
... rods: Stretching, bending and torsion, Equations of motion. Elastic waves, Conservative systems, Lagrangian and Hamiltonian formalisms; 2. Hydrodynamics: The velocity and density fields. Continuity equation, Pascals Law and the stress tensor, Bernoullis principle, Euler equations. Gravity waves, Vis ...
... rods: Stretching, bending and torsion, Equations of motion. Elastic waves, Conservative systems, Lagrangian and Hamiltonian formalisms; 2. Hydrodynamics: The velocity and density fields. Continuity equation, Pascals Law and the stress tensor, Bernoullis principle, Euler equations. Gravity waves, Vis ...
Topological quantum field theory
... ideas on each side and appears to be extremely deep. The traditional links between the two subjects, as embodied for example in Einstein's Theory of General Relativity or in Maxwell's Equations for Electro-Magnetism are concerned essentially with classical fields of force, governed by differential e ...
... ideas on each side and appears to be extremely deep. The traditional links between the two subjects, as embodied for example in Einstein's Theory of General Relativity or in Maxwell's Equations for Electro-Magnetism are concerned essentially with classical fields of force, governed by differential e ...
Topological quantum field theory
... ideas on each side and appears to be extremely deep. The traditional links between the two subjects, as embodied for example in Einstein's Theory of General Relativity or in Maxwell's Equations for Electro-Magnetism are concerned essentially with classical fields of force, governed by differential e ...
... ideas on each side and appears to be extremely deep. The traditional links between the two subjects, as embodied for example in Einstein's Theory of General Relativity or in Maxwell's Equations for Electro-Magnetism are concerned essentially with classical fields of force, governed by differential e ...
Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective
... (QEC) is the ‘‘threshold theorem’’ [1]. Even though QEC is a perturbative method [1,2], the threshold theorem states that, provided the noise strength is below a critical value, quantum information can be protected for arbitrarily long times. This remarkable theorem was first derived for stochastic ...
... (QEC) is the ‘‘threshold theorem’’ [1]. Even though QEC is a perturbative method [1,2], the threshold theorem states that, provided the noise strength is below a critical value, quantum information can be protected for arbitrarily long times. This remarkable theorem was first derived for stochastic ...
Krishnendu-Sengupta
... Consider a linear ramp of J(t)=Ji +(Jf - Ji) t/t. For dynamics, one needs to solve the Sch. Eq. Make a time dependent transformation to address the dynamics by projecting on the instantaneous low-energy sector. The method provides an accurate description of the ramp if J(t)/U <<1 and hence can treat ...
... Consider a linear ramp of J(t)=Ji +(Jf - Ji) t/t. For dynamics, one needs to solve the Sch. Eq. Make a time dependent transformation to address the dynamics by projecting on the instantaneous low-energy sector. The method provides an accurate description of the ramp if J(t)/U <<1 and hence can treat ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.