A Manifestation toward the Nambu-Goldstone Geometry
... defined over a usual topological space with a Euclidean norm ( an induced topology by a Lie group ). A Riemannian manifold is characterized by the following notions: Metric and tangent spaces, submanifolds and covering spaces, connections and bundles, several curvatures, geodesics, Laplacians, expon ...
... defined over a usual topological space with a Euclidean norm ( an induced topology by a Lie group ). A Riemannian manifold is characterized by the following notions: Metric and tangent spaces, submanifolds and covering spaces, connections and bundles, several curvatures, geodesics, Laplacians, expon ...
Quantum Computer Compilers
... Adiabatic Quantum Computing • Quantum computations can be implemented by the adiabatic evolution of the Hamiltonian of a quantum system • To solve a given problem we initialize the system to the ground state of a simple Hamiltonian • We then evolve the Hamiltonian to one whose ground state encodes ...
... Adiabatic Quantum Computing • Quantum computations can be implemented by the adiabatic evolution of the Hamiltonian of a quantum system • To solve a given problem we initialize the system to the ground state of a simple Hamiltonian • We then evolve the Hamiltonian to one whose ground state encodes ...
The Emergence of a Coupled Quantum Dot Array in a Doped Silicon
... for lithographically defined1-4 QDs and dots along a wire21,22 but also for chemically synthesized colloidal dots,10,12 ordinary molecules,43-45 and carbon nanotubes.20 The diamond structure is best seen when the coupling to the left and right electrodes is about equal and weak enough so that the de ...
... for lithographically defined1-4 QDs and dots along a wire21,22 but also for chemically synthesized colloidal dots,10,12 ordinary molecules,43-45 and carbon nanotubes.20 The diamond structure is best seen when the coupling to the left and right electrodes is about equal and weak enough so that the de ...
The AdS/CFT Correspondence arXiv:1501.00007
... its universally recognized elegance, until recently general relativity has been used by a relatively small subset of the scientific community – much smaller, for instance, than those using quantum mechanics or quantum field theory – mostly1 restricted to relativists, cosmologists, and a fraction of ...
... its universally recognized elegance, until recently general relativity has been used by a relatively small subset of the scientific community – much smaller, for instance, than those using quantum mechanics or quantum field theory – mostly1 restricted to relativists, cosmologists, and a fraction of ...
Nondegeneracy of the Lump Solution to the KP-I Equation
... Then ϕ = c1 ∂x Q + c2 ∂y Q, for certain constants c1 , c2 . Theorem 1 has long been conjectured to be true. See the remark after Lemma 7 in [30] concerning the spectral property and its relation to stability. We also expect that the linearized operator around Q has exactly one negative eigenvalue. B ...
... Then ϕ = c1 ∂x Q + c2 ∂y Q, for certain constants c1 , c2 . Theorem 1 has long been conjectured to be true. See the remark after Lemma 7 in [30] concerning the spectral property and its relation to stability. We also expect that the linearized operator around Q has exactly one negative eigenvalue. B ...
Stability conditions of diatomic molecules in
... applications in estimating atomic sizes by exploiting Raman spectroscopy [1], producing high fidelity binary shaped laser pulses for quantum logic gates [2], identifying pseudodiatomic behavior in polyatomic bond dissociation [3], and studying molecular potentials of isolated species [4]. The main a ...
... applications in estimating atomic sizes by exploiting Raman spectroscopy [1], producing high fidelity binary shaped laser pulses for quantum logic gates [2], identifying pseudodiatomic behavior in polyatomic bond dissociation [3], and studying molecular potentials of isolated species [4]. The main a ...
Duncan-Dunne-LINCS-2016-Interacting
... observables. The second requires that the observables be strongly complementary; this means their corresponding Frobenius algebras jointly form a Hopf algebra [13, 16]. The additional structure allows us to construct a ring of endomorphisms of the generator, distinct from the phase groups, and a lar ...
... observables. The second requires that the observables be strongly complementary; this means their corresponding Frobenius algebras jointly form a Hopf algebra [13, 16]. The additional structure allows us to construct a ring of endomorphisms of the generator, distinct from the phase groups, and a lar ...
Atomic Structure Institute of Lifelong Learning, University of Delhi
... of these scientists were rejected later but all of them were significant contributions in the progress of science and were a major breakthrough in their times. ...
... of these scientists were rejected later but all of them were significant contributions in the progress of science and were a major breakthrough in their times. ...
Conference booklet - XXXV Workshop on Geometric Methods in
... forms present in equations of motion, or alternatively, to a corresponding shift in degrees of relevant objects in action integral for Nambu mechanics. ...
... forms present in equations of motion, or alternatively, to a corresponding shift in degrees of relevant objects in action integral for Nambu mechanics. ...
Large-N Limit as a Classical Limit: Baryon Two-dimensional QCD and Multi-Matrix Models
... Spectacular experimental discoveries, such as patterns found in the hadronic spectrum [40, 83], electroweak gauge bosons [89], and scaling in deep inelastic scattering [38], parallel the discovery of the detailed orbits of planets and moons, or of discrete atomic spectra. On the other hand, equally ...
... Spectacular experimental discoveries, such as patterns found in the hadronic spectrum [40, 83], electroweak gauge bosons [89], and scaling in deep inelastic scattering [38], parallel the discovery of the detailed orbits of planets and moons, or of discrete atomic spectra. On the other hand, equally ...
Document
... Decoherence = loss of information stored in a qubit. Classical picture of environment: Fluctuation of Hamiltonian Quantum mechanical picture: Entanglement with environment Quantum mechanical picture: Entanglement with environment. ...
... Decoherence = loss of information stored in a qubit. Classical picture of environment: Fluctuation of Hamiltonian Quantum mechanical picture: Entanglement with environment Quantum mechanical picture: Entanglement with environment. ...
Phys. Rev. Lett. 110, 156402 - Institute for Quantum Optics and
... provided the total angular momentum J is conserved, we obtain a term / Jz2 corresponding to the one-axis twisting Hamiltonian [30]. To generate a spin squeezed state, we initialize the ensemble in a coherent spin state (CSS) j c 0 i along the x axis of the collective Bloch sphere. The CSS satisfies ...
... provided the total angular momentum J is conserved, we obtain a term / Jz2 corresponding to the one-axis twisting Hamiltonian [30]. To generate a spin squeezed state, we initialize the ensemble in a coherent spin state (CSS) j c 0 i along the x axis of the collective Bloch sphere. The CSS satisfies ...
Core Problem - Max-Planck
... “What would be most interesting, however, is if our result were to point to a physics beyond the standard model,” says Randolf Pohl. The standard model of particle physics describes all elementary particles and most of the forces between them. It covers most observations very well, but it also has s ...
... “What would be most interesting, however, is if our result were to point to a physics beyond the standard model,” says Randolf Pohl. The standard model of particle physics describes all elementary particles and most of the forces between them. It covers most observations very well, but it also has s ...
pdf
... a lower bound of Ω(|V |) on the query complexity. A natural question to ask in our context is whether allowing quantum queries can reduce the query complexity of testing graph isomorphism. A quantum query to the adjacency matrix of a graph G can be of the form |i, ji|bi 7→ |i, ji|b ⊕ G(i, j)i, where ...
... a lower bound of Ω(|V |) on the query complexity. A natural question to ask in our context is whether allowing quantum queries can reduce the query complexity of testing graph isomorphism. A quantum query to the adjacency matrix of a graph G can be of the form |i, ji|bi 7→ |i, ji|b ⊕ G(i, j)i, where ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.