Explicit construction of linear sized tolerant networks
... subgraph H such that for every vertex-set S of H the number of edges incident to vertices in S is at least d IS(/2. Next we need a relation between the eigenvalues of a graph G and the density of its induced subgraphs. Let A =Ao be the n by n adjacency matrix of a d-regular graph G = (V, E) on V = ( ...
... subgraph H such that for every vertex-set S of H the number of edges incident to vertices in S is at least d IS(/2. Next we need a relation between the eigenvalues of a graph G and the density of its induced subgraphs. Let A =Ao be the n by n adjacency matrix of a d-regular graph G = (V, E) on V = ( ...
Boson sampling for molecular vibronic spectra - CIQM
... in chemistry and biology; for example, the photodamage of deoxyribonucleic acid molecules is fatal to life. We show a photoelectron spectrum of thymine29 (the experimental spectrum is also given later in Fig. 4) as an example of the current state of the art. We propose a new simulation scheme that p ...
... in chemistry and biology; for example, the photodamage of deoxyribonucleic acid molecules is fatal to life. We show a photoelectron spectrum of thymine29 (the experimental spectrum is also given later in Fig. 4) as an example of the current state of the art. We propose a new simulation scheme that p ...
Two-resonator circuit quantum electrodynamics: Dissipative theory
... The resulting effective Hamiltonian describes a resonatorresonator interaction whose coefficient has two contributions. The first contribution depends on the qubit state and the qubit-resonator detuning and can have a positive or negative sign. The second one has a definite sign and stems from the f ...
... The resulting effective Hamiltonian describes a resonatorresonator interaction whose coefficient has two contributions. The first contribution depends on the qubit state and the qubit-resonator detuning and can have a positive or negative sign. The second one has a definite sign and stems from the f ...
Classical Mechanics - Manybody Physics Group.
... gives the extremal value of the action, then such path would be the physical path obeying Newton’s law. Hence, the entire classical mechanics can be formulated in terms of the new quantity, the action S, together with the variational principle. This we might state as an equally compelling formulatio ...
... gives the extremal value of the action, then such path would be the physical path obeying Newton’s law. Hence, the entire classical mechanics can be formulated in terms of the new quantity, the action S, together with the variational principle. This we might state as an equally compelling formulatio ...
Elements of QFT in Curved Space-Time
... non-Abelian vectors, since only the free parts are important. Consider a single Abelian vector. The action must be supplemented by the gauge fixing and ghost terms. The 1-loop contribution to the vacuum EA Γ̄(1) = ...
... non-Abelian vectors, since only the free parts are important. Consider a single Abelian vector. The action must be supplemented by the gauge fixing and ghost terms. The 1-loop contribution to the vacuum EA Γ̄(1) = ...
A definite resolution of the mystery of
... WMAP and supernova analysis. The rationale behind the basic idea of the proposed theory is simply put as follows: Einstein’s special relativity and consequently his equation E = mc2 may be considered from the view point of high energy particle physics as a one dimensional theory, i.e. a theory based ...
... WMAP and supernova analysis. The rationale behind the basic idea of the proposed theory is simply put as follows: Einstein’s special relativity and consequently his equation E = mc2 may be considered from the view point of high energy particle physics as a one dimensional theory, i.e. a theory based ...
Hamiltonian dynamics
... The choice of y0 determines the nature of the motion (in the sense of sect. 2.1.1): for y0 = 0 we have that every point on the y0 = 0 line is stationary, for y0 = p/q the motion is periodic, and for irrational y0 any choice of x0 leads to a quasiperiodic motion (see figure 8.5 (a)). Despite the simp ...
... The choice of y0 determines the nature of the motion (in the sense of sect. 2.1.1): for y0 = 0 we have that every point on the y0 = 0 line is stationary, for y0 = p/q the motion is periodic, and for irrational y0 any choice of x0 leads to a quasiperiodic motion (see figure 8.5 (a)). Despite the simp ...
Transport Properties of Interacting Edge Modes in 2D Topological
... but the spin Hall conductance is nite. In addition to that, potential disorder can not backscatter electrons, as it is unable to ip their spins. Localization therefore, does not occur in the presence of potential disorder only. In contrast, magnetic impurities can induce backscattering. A recent wor ...
... but the spin Hall conductance is nite. In addition to that, potential disorder can not backscatter electrons, as it is unable to ip their spins. Localization therefore, does not occur in the presence of potential disorder only. In contrast, magnetic impurities can induce backscattering. A recent wor ...
Gap Evolution in \nu=1/2 Bilayer Quantum Hall Systems
... and Pf , and proposed a d–SAS phase diagram.17) Pursuing this scenario, Ho argued interesting connections between these 1=2 FQHE states and superfluid 3 He.18) Namely, 331 and Pf correspond to the ABM state and A1 state, respectively, and the introduction of SAS corresponds to the Zeeman splitti ...
... and Pf , and proposed a d–SAS phase diagram.17) Pursuing this scenario, Ho argued interesting connections between these 1=2 FQHE states and superfluid 3 He.18) Namely, 331 and Pf correspond to the ABM state and A1 state, respectively, and the introduction of SAS corresponds to the Zeeman splitti ...
Three-sublattice order in the SU (3) Heisenberg model on the
... higher-order quantum fluctuations, or if in this case another state is selected. An example of such a scenario has recently been observed in the SU(4) Heisenberg model on the square lattice,24 where low-order quantum fluctuations select a plaquette state, but additional higher-order quantum fluctuat ...
... higher-order quantum fluctuations, or if in this case another state is selected. An example of such a scenario has recently been observed in the SU(4) Heisenberg model on the square lattice,24 where low-order quantum fluctuations select a plaquette state, but additional higher-order quantum fluctuat ...
Entanglement Entropy
... Let’s consider a quantum system: we usually identify it through its state, i.e. its wave function. In this way, we assume it is possible to define the system completely and build the function which represents it. However, this is not always feasible. For instance, in an electron-target scattering ex ...
... Let’s consider a quantum system: we usually identify it through its state, i.e. its wave function. In this way, we assume it is possible to define the system completely and build the function which represents it. However, this is not always feasible. For instance, in an electron-target scattering ex ...
3, Coherent and Squeezed States 1. Coherent states 2. Squeezed
... Attenuation of Coherent States Glauber showed that a classical oscillating current in free space produces a multimode coherent state of light. The quantum noise of a laser operating at far above threshold is close to that of a coherent state. A coherent state does not change its quantum noise prope ...
... Attenuation of Coherent States Glauber showed that a classical oscillating current in free space produces a multimode coherent state of light. The quantum noise of a laser operating at far above threshold is close to that of a coherent state. A coherent state does not change its quantum noise prope ...
Quantum scattering
... potential requires special care.) The hope is that in the limit R → ∞ we will recover the scattering system. But some care is required in implementing this. The smooth Weyl term d̄(E; R) belonging to our box with the enclosed potential V diverges for a spherical 2-dimensional box of radius R quadrat ...
... potential requires special care.) The hope is that in the limit R → ∞ we will recover the scattering system. But some care is required in implementing this. The smooth Weyl term d̄(E; R) belonging to our box with the enclosed potential V diverges for a spherical 2-dimensional box of radius R quadrat ...
Covering Graph for Diagram Groups from Semigroup
... e . Then regarding e as a path of length 1, we know that e , and e , are lifts of e at a . Hence by theorem (2.10) e , e , that is Ω is locally injective. Now choose a be any vertex of Γ and e star a . Regarding e as a path of length 1, then by theorem (2.11) there exists at least one lift of this p ...
... e . Then regarding e as a path of length 1, we know that e , and e , are lifts of e at a . Hence by theorem (2.10) e , e , that is Ω is locally injective. Now choose a be any vertex of Γ and e star a . Regarding e as a path of length 1, then by theorem (2.11) there exists at least one lift of this p ...
Quantum Thermodynamics - Open Research Exeter
... One of the biggest puzzles in quantum theory today is to show how the well-studied properties of a few particles translate into a statistical theory from which new macroscopic quantum thermodynamic laws emerge. This challenge is addressed by the emerging field of quantum thermodynamics which has gro ...
... One of the biggest puzzles in quantum theory today is to show how the well-studied properties of a few particles translate into a statistical theory from which new macroscopic quantum thermodynamic laws emerge. This challenge is addressed by the emerging field of quantum thermodynamics which has gro ...
