THE TRIANGLE INEQUALITY AND THE DUAL GROMOV
... spaces into a third compact metric space to the noncommutative world. If ιX : X ,→ Z is an isometry from a compact metric space (X, dX ) into a compact metric space (Z, dZ ), and if f : X → R is a Lipschitz function, then McShane’s Theorem [15] provides us with a function g : Z → R such that g ◦ ιX ...
... spaces into a third compact metric space to the noncommutative world. If ιX : X ,→ Z is an isometry from a compact metric space (X, dX ) into a compact metric space (Z, dZ ), and if f : X → R is a Lipschitz function, then McShane’s Theorem [15] provides us with a function g : Z → R such that g ◦ ιX ...
Chemical reaction rates using the semiclassical
... 共SC-IVR兲 expression without invoking the linearization approximation has been the forward-backward IVR.22 The FBIVR combines the forward and backward time evolution operators into one semiclassical time propagation; as a result the FB-IVR integrand is considerably less oscillatory. However, the FB-I ...
... 共SC-IVR兲 expression without invoking the linearization approximation has been the forward-backward IVR.22 The FBIVR combines the forward and backward time evolution operators into one semiclassical time propagation; as a result the FB-IVR integrand is considerably less oscillatory. However, the FB-I ...
Including quantum effects in the dynamics of complex „i.e., large
... input into a multidimensional generalization of the WKB approximation.兲 Since this description includes interference and tunneling 共or classically forbidden processes in general, which arise as the analytic continuation of interference兲, all quantum effects in molecular dynamics are incorporated in ...
... input into a multidimensional generalization of the WKB approximation.兲 Since this description includes interference and tunneling 共or classically forbidden processes in general, which arise as the analytic continuation of interference兲, all quantum effects in molecular dynamics are incorporated in ...
Quantum electrical transport in samples of limited
... 2~a! is an example of the relevant observations published in 1988 by two groups, one at the Phillips Research Laboratories2 and one at the Cavendish Laboratory in Cambridge.3 In these measurements, there is no magnetic field applied. Figure 2~b! sketches the experimental arrangement needed to genera ...
... 2~a! is an example of the relevant observations published in 1988 by two groups, one at the Phillips Research Laboratories2 and one at the Cavendish Laboratory in Cambridge.3 In these measurements, there is no magnetic field applied. Figure 2~b! sketches the experimental arrangement needed to genera ...
Multiphoton population transfer between rovibrational states of HF: adiabatic
... used in figure 1 by a factor of 5 down to 1 × 1013 W cm−2 results in only ∼4% transition probability into ν = 4, and rest of the population stays in the initial ν = 0 state. Note that this only corresponds to a decrease in the peak field strength by a factor of ∼2.2. At this point, doubling the carr ...
... used in figure 1 by a factor of 5 down to 1 × 1013 W cm−2 results in only ∼4% transition probability into ν = 4, and rest of the population stays in the initial ν = 0 state. Note that this only corresponds to a decrease in the peak field strength by a factor of ∼2.2. At this point, doubling the carr ...
Slides - Agenda
... An exact procedure for computing many-particle Bohmian trajectories The correlations are introduced into the time-dependent potentials 4th The interacting potential from (a classical-like) Bohmian trajectories 5th There is a real potential to account for “non-classical” correlations 6th There is a i ...
... An exact procedure for computing many-particle Bohmian trajectories The correlations are introduced into the time-dependent potentials 4th The interacting potential from (a classical-like) Bohmian trajectories 5th There is a real potential to account for “non-classical” correlations 6th There is a i ...
Loop Quantum Gravity in a Nutshell
... • However, iteration results in “run-away” solutions (related to nonrenormalizabality). ...
... • However, iteration results in “run-away” solutions (related to nonrenormalizabality). ...
3. Traditional Models of Computation - UF CISE
... sufficiently small, which has not yet been accomplished, but which may be in the future. Theoretical models of computing—Key model components. Now, what do we mean by a theoretical model of computing? In general, a theoretical model of any size computer (whether “nano” or not) can involve a number o ...
... sufficiently small, which has not yet been accomplished, but which may be in the future. Theoretical models of computing—Key model components. Now, what do we mean by a theoretical model of computing? In general, a theoretical model of any size computer (whether “nano” or not) can involve a number o ...
Quantum Private Information Retrieval - UvA/FNWI
... misfortune is that when we “look” (measure) at such a state it collapses to one of two basis states and all the information which was contained in the superposition ...
... misfortune is that when we “look” (measure) at such a state it collapses to one of two basis states and all the information which was contained in the superposition ...
Quantum fluctuation relations: Foundations and applications
... where z ¼ ðq; pÞ denotes a point in the phase space of the considered system. In the following we assume that the force acts within a temporal interval set by a starting time 0 and a final time . The instantaneous force values t are specified by a function , which we refer to as the force protoco ...
... where z ¼ ðq; pÞ denotes a point in the phase space of the considered system. In the following we assume that the force acts within a temporal interval set by a starting time 0 and a final time . The instantaneous force values t are specified by a function , which we refer to as the force protoco ...
Distance between quantum states in the presence of initial qubit
... contractive with respect to some metrics. In consequence, the distance D[ρ1 ,ρ2 ] between two states can tend to zero when the system approaches a unique steady state (i.e., the dynamics is relaxing). We emphasize that contractivity is not a universal feature but depends on the metric: Quantum evolu ...
... contractive with respect to some metrics. In consequence, the distance D[ρ1 ,ρ2 ] between two states can tend to zero when the system approaches a unique steady state (i.e., the dynamics is relaxing). We emphasize that contractivity is not a universal feature but depends on the metric: Quantum evolu ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.