The 11 most beautiful equations in mathematics General relativity
... This simple formula encapsulates something pure about the nature of spheres: "It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces ...
... This simple formula encapsulates something pure about the nature of spheres: "It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces ...
Slide - Pacific Institute of Theoretical Physics
... one is the existence of phase transitions. Physicists have turned this into a virtue, by analysing the way the effective Hamiltonian changes as one approaches a finite-T critical point. One gets “Universality Classes” of effective Hamiltonian, describing many different systems, as they approach the ...
... one is the existence of phase transitions. Physicists have turned this into a virtue, by analysing the way the effective Hamiltonian changes as one approaches a finite-T critical point. One gets “Universality Classes” of effective Hamiltonian, describing many different systems, as they approach the ...
Folds, Bosonization and non-triviality of the classical limit of 2D
... It is well known that powers of β± satisfy a w∞ algebra. In this construction the w±,n themselves satisfy an independent w∞ algebra. 2 So far our considerations were independent of the fermion dynamics. Given the hamiltonian we can now obtain the time evolution equations for the quantities β± , w±,n ...
... It is well known that powers of β± satisfy a w∞ algebra. In this construction the w±,n themselves satisfy an independent w∞ algebra. 2 So far our considerations were independent of the fermion dynamics. Given the hamiltonian we can now obtain the time evolution equations for the quantities β± , w±,n ...
The Path Integral approach to Quantum Mechanics Lecture Notes
... • What adds up is the amplitude Φ and not the probability density itself. • The difference between classical and quantum composition of probabilities is given by the interference between classically distinct trajectories. In the standard approach to Quantum Mechanics, the probability amplitude is de ...
... • What adds up is the amplitude Φ and not the probability density itself. • The difference between classical and quantum composition of probabilities is given by the interference between classically distinct trajectories. In the standard approach to Quantum Mechanics, the probability amplitude is de ...
Academia Sinica, Taipei, Taiwan, 06/2010, Yip Sungkit
... The leading mesoscopic corrections contained in (0) are larger The correction to (0) proportional to has different sign ...
... The leading mesoscopic corrections contained in (0) are larger The correction to (0) proportional to has different sign ...
manuscript
... Quantum entanglement properties of the pseudo-spin representation of the BCS model is investigated. In case of degenerate energy levels, where wave functions take a particularly simple form, spontaneous breaking of exchange symmetry under local noise is studied. Even if the Hamiltonian has the same ...
... Quantum entanglement properties of the pseudo-spin representation of the BCS model is investigated. In case of degenerate energy levels, where wave functions take a particularly simple form, spontaneous breaking of exchange symmetry under local noise is studied. Even if the Hamiltonian has the same ...
ABSTRACTS Workshop on “Higher topological quantum field theory
... Interacting Frobenius Algebras Are Hopf Commutative Frobenius algebras play an important role in both TQFT and CQM; in the first case they correspond to 2d TQFTs, while in the second they are non-degenerate observables. I will consider the case of “special” Frobenius algebras, and their associated g ...
... Interacting Frobenius Algebras Are Hopf Commutative Frobenius algebras play an important role in both TQFT and CQM; in the first case they correspond to 2d TQFTs, while in the second they are non-degenerate observables. I will consider the case of “special” Frobenius algebras, and their associated g ...
a Multicromophoric approach to describe the energy
... Another approximation widely used in literature [13][14] is ignoring the off diagonal terms in the equations leading to the calculations of the lineshapes operators (Secular approximation). Our technique based on analytical continuation and time convolutionless master equation doesn’t use this appro ...
... Another approximation widely used in literature [13][14] is ignoring the off diagonal terms in the equations leading to the calculations of the lineshapes operators (Secular approximation). Our technique based on analytical continuation and time convolutionless master equation doesn’t use this appro ...
EMPS - Module - MAS2016 Methods for Differential Equations
... techniques are used extensively in subsequent modules in Applied Mathematics, for example in Hydrodynamics and Quantum theory. Topics covered include: Second order ordinary differential equations; Method of Frobenius and Variation of Parameters; Special functions, with emphasis on Legendre polynomia ...
... techniques are used extensively in subsequent modules in Applied Mathematics, for example in Hydrodynamics and Quantum theory. Topics covered include: Second order ordinary differential equations; Method of Frobenius and Variation of Parameters; Special functions, with emphasis on Legendre polynomia ...
8 Lecture 8: Periodic motion about an equilibrium point
... The conclusion is�that with the particular potential (151) the period of oscillations is as given in (152), namely, m ∆tx1 →x2 →x1 = π 2b . Remarkably, in this case the period of oscillations does not depend at all on the energy E nor on the parameter a (which determines the steepness of the potenti ...
... The conclusion is�that with the particular potential (151) the period of oscillations is as given in (152), namely, m ∆tx1 →x2 →x1 = π 2b . Remarkably, in this case the period of oscillations does not depend at all on the energy E nor on the parameter a (which determines the steepness of the potenti ...
The Higgs Boson and Electroweak Symmetry Breaking
... In this lecture, I have described 4 possible models of EWSB. We do not know whether the Higgs boson is elementary or composite; I have presented models of both types. In each model, the Higgs boson is part of a larger superstructure that will be revealed when we experiment at multi-100 GeV eneriges ...
... In this lecture, I have described 4 possible models of EWSB. We do not know whether the Higgs boson is elementary or composite; I have presented models of both types. In each model, the Higgs boson is part of a larger superstructure that will be revealed when we experiment at multi-100 GeV eneriges ...
Presentazione di PowerPoint - INAF - OA
... and the SRD approximation In order to solve the equation of motion of Φ we have to specify a particular form of the potential. Different forms of V(Φ) have been explored during the years and each of them produces a different type of expansion of the universe. Requirements on V(Φ) : 1.In order to ...
... and the SRD approximation In order to solve the equation of motion of Φ we have to specify a particular form of the potential. Different forms of V(Φ) have been explored during the years and each of them produces a different type of expansion of the universe. Requirements on V(Φ) : 1.In order to ...
The Free Particle – Applying and Expanding
... motion due to a constant force (constant acceleration). In quantum physics in order to get a “simple” case we have to take a step back to motion due to a no force (which is the even simpler case of constant velocity motion in classical physics). In classical physics there is an even simpler case tha ...
... motion due to a constant force (constant acceleration). In quantum physics in order to get a “simple” case we have to take a step back to motion due to a no force (which is the even simpler case of constant velocity motion in classical physics). In classical physics there is an even simpler case tha ...
Effective Topological Field Theories in Condensed Matter Physics
... The search for new states of matter The search for new elements led to a golden age of chemistry. The search for new particles led to the golden age of particle physics. In condensed matter physics, we ask what are the fundamental states of matter? In the classical world we have solid, liquid and g ...
... The search for new states of matter The search for new elements led to a golden age of chemistry. The search for new particles led to the golden age of particle physics. In condensed matter physics, we ask what are the fundamental states of matter? In the classical world we have solid, liquid and g ...
Broken symmetry revisited - Homepages of UvA/FNWI staff
... Moreover, if a charge corresponding to some representation Γ of H is transported around a vortex carrying the magnetic flux h ∈ H, it returns transformed by the matrix Γ(h) assigned to the element h in the representation Γ of H. The spontaneously broken 2+1 dimensional models just mentioned will be ...
... Moreover, if a charge corresponding to some representation Γ of H is transported around a vortex carrying the magnetic flux h ∈ H, it returns transformed by the matrix Γ(h) assigned to the element h in the representation Γ of H. The spontaneously broken 2+1 dimensional models just mentioned will be ...
125 GeV higgs in supersymmetry
... ELEMENTARY HIGGS BOSON PREDICTED BY THE SM IS DISCOVERED! „APPARENTLY JUST” IS VERY IMPORTANT! ...
... ELEMENTARY HIGGS BOSON PREDICTED BY THE SM IS DISCOVERED! „APPARENTLY JUST” IS VERY IMPORTANT! ...
N =1
... The theory is supersymmetric but its ground state is not. (This nonzero vacuum energy should not be confused with the cosmological constant. The latter can be adjusted to its desired value.) ...
... The theory is supersymmetric but its ground state is not. (This nonzero vacuum energy should not be confused with the cosmological constant. The latter can be adjusted to its desired value.) ...