Different faces of integrability in the gauge theories or in the jungles
... The very surface has even more “physical” interpretation – this is the surface we would live on if we would enjoy N=2 SUSY. Any “N=2 citizen” lives on the 5+1 worldvolume of the soliton(M5 brane) in higher dimensions which looks as R(3,1)+(Riemann surface). Is it possible to derive integrable sy ...
... The very surface has even more “physical” interpretation – this is the surface we would live on if we would enjoy N=2 SUSY. Any “N=2 citizen” lives on the 5+1 worldvolume of the soliton(M5 brane) in higher dimensions which looks as R(3,1)+(Riemann surface). Is it possible to derive integrable sy ...
From Quantum Mechanics to String Theory
... consider the particle Δ++, made up of three “u” quarks it is a spin 3/2 particle, capable of carrying angular momentum in the z-direction equivalent to all three quarks having spin in the same direction (+++) it looks as if we have three identical quarks, all in the same spin state (u,+) there must ...
... consider the particle Δ++, made up of three “u” quarks it is a spin 3/2 particle, capable of carrying angular momentum in the z-direction equivalent to all three quarks having spin in the same direction (+++) it looks as if we have three identical quarks, all in the same spin state (u,+) there must ...
Simulating large quantum circuits on a small quantum computer
... |ΦU i = (I ⊗ U )|Φi/ 2 is a quantum encoding of U, i.e., a static way to store a dynamic resource! Given |ΦU i, we can execute U. So |ΦU i is a form of “quantum software” [Pre99, GC99]. In a similar spirit, a mixed state ρ encodes a Hamiltonian that can be executed if given enough copies of ρ [KLL+ ...
... |ΦU i = (I ⊗ U )|Φi/ 2 is a quantum encoding of U, i.e., a static way to store a dynamic resource! Given |ΦU i, we can execute U. So |ΦU i is a form of “quantum software” [Pre99, GC99]. In a similar spirit, a mixed state ρ encodes a Hamiltonian that can be executed if given enough copies of ρ [KLL+ ...
Many-Body Localization
... • Needs to be local – measure with few-body operators. E.g. compact in real-space ...
... • Needs to be local – measure with few-body operators. E.g. compact in real-space ...
by Dr. Matti Pitkänen
... oscillator approximation does not make sense. And it is not obvious whether one can make the metaphor of BE condensation a precise concept. The formation of habit at the level of species could be analogous to the formation of repetitive pattern in Benard-flow, when external entropy feed exceeds some ...
... oscillator approximation does not make sense. And it is not obvious whether one can make the metaphor of BE condensation a precise concept. The formation of habit at the level of species could be analogous to the formation of repetitive pattern in Benard-flow, when external entropy feed exceeds some ...
hosted here - Jeffrey C. Morton
... g can be composed to get a arrow f ◦ g as long as the source object of f is the same as the target object of g. Categorification is not a systematic process, and as a form of explanation we should not expect it to be: given an arbitrary collection of facts, there is no standard way to find an explan ...
... g can be composed to get a arrow f ◦ g as long as the source object of f is the same as the target object of g. Categorification is not a systematic process, and as a form of explanation we should not expect it to be: given an arbitrary collection of facts, there is no standard way to find an explan ...
Quantum One-Way Communication is Exponentially Stronger Than
... See also [Mon10] for a similar separation. Another closely related result is by Gavinsky [Gav08], who improved on Bar-Yossef et al.’s [BJK04] result in the other direction: namely, he showed an exponential separation between one-way quantum communication and two-way classical communication (just as ...
... See also [Mon10] for a similar separation. Another closely related result is by Gavinsky [Gav08], who improved on Bar-Yossef et al.’s [BJK04] result in the other direction: namely, he showed an exponential separation between one-way quantum communication and two-way classical communication (just as ...
m NV Centers in Quantum Information Technology ! De-Coherence Protection &
... uantum control pulses and NV centers appear as y level diagrams of the NV center electron spin agnetic field splits the NV spin triplet electronic d by the spin sublevels mS = 0 (labeled j0〉) and NV1. For the pulsed experiments, the same Rabi ...
... uantum control pulses and NV centers appear as y level diagrams of the NV center electron spin agnetic field splits the NV spin triplet electronic d by the spin sublevels mS = 0 (labeled j0〉) and NV1. For the pulsed experiments, the same Rabi ...
Interaction-induced Lipkin-Meshkov-Glick model in a Bose
... This not only gives rise to a new regime of cavity quantum electradynamics, in which all atoms occupying a single mode of a matter-wave field can couple identically to the photon induced by the cavity mode, but also opens possibilities to a wealth of new phenomena that can be expected in the cavity- ...
... This not only gives rise to a new regime of cavity quantum electradynamics, in which all atoms occupying a single mode of a matter-wave field can couple identically to the photon induced by the cavity mode, but also opens possibilities to a wealth of new phenomena that can be expected in the cavity- ...
Complexity Limitations on Quantum Computation 1 Introduction
... The class PP was first defined by Gill [Gil77] as probabilistic polynomial time with unbounded error. Definition 2.3, first given by Fenner, Fortnow, and Kurtz [FFK94], makes the class considerably easier to work with. Definition 2.4 The class LWPP consists of those languages L such that for some Ga ...
... The class PP was first defined by Gill [Gil77] as probabilistic polynomial time with unbounded error. Definition 2.3, first given by Fenner, Fortnow, and Kurtz [FFK94], makes the class considerably easier to work with. Definition 2.4 The class LWPP consists of those languages L such that for some Ga ...
An Improved Quantum Algorithm for Searching an Ordered List
... from (29), ensuring that the pairs of coefficients a,r and a,N −r , and b,r and b,N −r , are each treated as a single variable to respect the symmetries in (20) and (21). Once we have found the gradient, we reduce the problem to a one-dimensional search along this vector to find a new C for which ...
... from (29), ensuring that the pairs of coefficients a,r and a,N −r , and b,r and b,N −r , are each treated as a single variable to respect the symmetries in (20) and (21). Once we have found the gradient, we reduce the problem to a one-dimensional search along this vector to find a new C for which ...
Paper
... This system now has time-reversal symmetry, in contrast to the system with the same synthetic magnetic field for both states (since a magnetic field breaks time-reversal symmetry). This scheme implements spin-orbit coupling both in two and three dimensions and with bosons and fermions. For fermions, ...
... This system now has time-reversal symmetry, in contrast to the system with the same synthetic magnetic field for both states (since a magnetic field breaks time-reversal symmetry). This scheme implements spin-orbit coupling both in two and three dimensions and with bosons and fermions. For fermions, ...
Orthogonal Polynomials 1 Introduction 2 Orthogonal Polynomials
... Any polynomial f (x) of degree nPcan be expanded in terms of p0 p1 : : : pn , that is, there exist coecients ai such that f (x) = ni=0 ai pi (x). Given an orthogonal set of polynomials fp0 (x) p1 (x) : : :g, each polynomial, pk (x) is orthogonal to any polynomial of degree < k. Any orthogonal set o ...
... Any polynomial f (x) of degree nPcan be expanded in terms of p0 p1 : : : pn , that is, there exist coecients ai such that f (x) = ni=0 ai pi (x). Given an orthogonal set of polynomials fp0 (x) p1 (x) : : :g, each polynomial, pk (x) is orthogonal to any polynomial of degree < k. Any orthogonal set o ...
CHAPTER 16: Quantum Mechanics and the Hydrogen Atom
... distance of electrons from the nucleus (& the size of the orbital). 3s larger than 2s. • Ψnlm has l angular nodes and n-l-1 radial nodes (total of n-1 nodes) • Only for s orbitals does Ψnlm remain nonzero as r→0. Only s orbitals “penetrate to the nucleus” • Note: orbitals are only rigorous for H ato ...
... distance of electrons from the nucleus (& the size of the orbital). 3s larger than 2s. • Ψnlm has l angular nodes and n-l-1 radial nodes (total of n-1 nodes) • Only for s orbitals does Ψnlm remain nonzero as r→0. Only s orbitals “penetrate to the nucleus” • Note: orbitals are only rigorous for H ato ...
Bell's theorem
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Bell's theorem is a ‘no-go theorem’ that draws an important distinction between quantum mechanics (QM) and the world as described by classical mechanics. This theorem is named after John Stewart Bell.In its simplest form, Bell's theorem states:Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from ""indifference"" to ""wild extravagance"". Lawrence Berkeley particle physicist Henry Stapp declared: ""Bell's theorem is the most profound discovery of science.""Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables). Bell concluded:Bell summarized one of the least popular ways to address the theorem, superdeterminism, in a 1985 BBC Radio interview: