Representations of Lorentz and Poincaré groups
... is the Pauli-Lubanski pseudovector. We now consider two cases, depending on whether the particle in the 1-particle state |pi ∼ a†p |0i is massive or massless. • Massive representations: on a massive 1-particle state, P µ Pµ = P 2 has eigenvalue p2 = Ep2 − |p|2 = m2 where m is the mass of the particl ...
... is the Pauli-Lubanski pseudovector. We now consider two cases, depending on whether the particle in the 1-particle state |pi ∼ a†p |0i is massive or massless. • Massive representations: on a massive 1-particle state, P µ Pµ = P 2 has eigenvalue p2 = Ep2 − |p|2 = m2 where m is the mass of the particl ...
Tight bounds on quantum searching
... a Grover iteration is performed: the total time needed is clearly in the order of that number. On the s–th time round the main loop, the value of m is λs−1 and the expected number of Grover iterations is less than half that value since j is chosen randomly so that 0 ≤ j < m. We say that the algorith ...
... a Grover iteration is performed: the total time needed is clearly in the order of that number. On the s–th time round the main loop, the value of m is λs−1 and the expected number of Grover iterations is less than half that value since j is chosen randomly so that 0 ≤ j < m. We say that the algorith ...
Document
... Inside the well the particle is “free”. This is because U (x) is zero inside the well. IncreasingU (x) to infinity as the width is reduced to zero, we have the idealization of an infinite potential square well. ...
... Inside the well the particle is “free”. This is because U (x) is zero inside the well. IncreasingU (x) to infinity as the width is reduced to zero, we have the idealization of an infinite potential square well. ...
98, 010506 (2007)
... using 40 K atoms, although the technique is applicable to other species as well. Suppose the atoms in the superfluid are in the 42 S1=2 hyperfine ground state jii jF 9=2; mF 7=2i in the case of p-wave resonance [9]. To determine whether there is an unpaired atom inside a composite vortex, a t ...
... using 40 K atoms, although the technique is applicable to other species as well. Suppose the atoms in the superfluid are in the 42 S1=2 hyperfine ground state jii jF 9=2; mF 7=2i in the case of p-wave resonance [9]. To determine whether there is an unpaired atom inside a composite vortex, a t ...
Fully nonlocal quantum correlations
... refer to Pauli matrices acting on qubits n = 1 and n = 2, which span a four-dimensional Hilbert space. Each group constitutes a complete set of mutually commuting (and therefore compatible) observables, defining thus a context. In this way, there are six contexts, and every observable belongs to two ...
... refer to Pauli matrices acting on qubits n = 1 and n = 2, which span a four-dimensional Hilbert space. Each group constitutes a complete set of mutually commuting (and therefore compatible) observables, defining thus a context. In this way, there are six contexts, and every observable belongs to two ...
PPT
... volume V, particle number N, density n=N/V, temperature T. Equation for the chemical potential closes the equilibrium problem: ...
... volume V, particle number N, density n=N/V, temperature T. Equation for the chemical potential closes the equilibrium problem: ...
Polynomial-Time Algorithms for Prime Factorization and Discrete
... is a basis vector of the Hilbert space. If the machine is measured (with respect to this basis) at any particular step, the probability of seeing basis state jSi i is jai j2 ; however, measuring the state of the machine projects this state to the observed basis vector jSi i. Thus, looking at the mac ...
... is a basis vector of the Hilbert space. If the machine is measured (with respect to this basis) at any particular step, the probability of seeing basis state jSi i is jai j2 ; however, measuring the state of the machine projects this state to the observed basis vector jSi i. Thus, looking at the mac ...
The capacity of the noisy quantum channel
... The ‘quantum’ in quantum mechanics means ‘how much’ — in quantum mechanics, classically continuous variables such as energy, angular momentum and charge come in discrete units called quanta. This discrete character of quantum-mechanical systems such as photons, atoms, and spins allows them to regist ...
... The ‘quantum’ in quantum mechanics means ‘how much’ — in quantum mechanics, classically continuous variables such as energy, angular momentum and charge come in discrete units called quanta. This discrete character of quantum-mechanical systems such as photons, atoms, and spins allows them to regist ...
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... 11], Hagedorn [7, 8], and Littlejohn [18, Section 7]; see also references therein. The most salient feature of the Gaussian wave packet is that it gives an exact solution to the Schrödinger equation with quadratic potentials, given that the parameters governing the dynamics of the wave packet follo ...
... 11], Hagedorn [7, 8], and Littlejohn [18, Section 7]; see also references therein. The most salient feature of the Gaussian wave packet is that it gives an exact solution to the Schrödinger equation with quadratic potentials, given that the parameters governing the dynamics of the wave packet follo ...
Topological Chern Indices in Molecular Spectra
... This result has been formulated in a more mathematical context by Bellissard [9] and by Zelditch [10] but was not published due to its “apparent mathematical simplicity.” We will prove formula (3) below. A few remarks are in order here. Since 共2j 1 1兲 is the number of quanta in the classical phase s ...
... This result has been formulated in a more mathematical context by Bellissard [9] and by Zelditch [10] but was not published due to its “apparent mathematical simplicity.” We will prove formula (3) below. A few remarks are in order here. Since 共2j 1 1兲 is the number of quanta in the classical phase s ...
Effective Field Theories
... of inverse mass (related to Einstein's famous formula : = ; 9 ). So again, if we are only viewing the low energy limit higher orders in energy will contribute little so in the end those terms can be neglected and we again can perform our renormalization procedure. That's the basic concept of an eff ...
... of inverse mass (related to Einstein's famous formula : = ; 9 ). So again, if we are only viewing the low energy limit higher orders in energy will contribute little so in the end those terms can be neglected and we again can perform our renormalization procedure. That's the basic concept of an eff ...
propagation methods for quantum molecular dynamics
... The operator I2I is a continuous generator of the evolution, and to fulfill the symmetryrequirement, I2I has to be Hermitian. Aside from this requirement, the operator I2I is unrestricted. The operator I21 is customarily identified with the Hamiltonian of the system, which means that its expectation ...
... The operator I2I is a continuous generator of the evolution, and to fulfill the symmetryrequirement, I2I has to be Hermitian. Aside from this requirement, the operator I2I is unrestricted. The operator I21 is customarily identified with the Hamiltonian of the system, which means that its expectation ...
boltzmann`s entropy and time`s arrow
... when this ratio is finite but very large; it is, however, clearly impossible when the system contains only one or a few particles. I use this example, despite its highly idealized nature, because here all the mathematical i's have been dotted. The Lorentz gas shows ipso facto, in a way that should c ...
... when this ratio is finite but very large; it is, however, clearly impossible when the system contains only one or a few particles. I use this example, despite its highly idealized nature, because here all the mathematical i's have been dotted. The Lorentz gas shows ipso facto, in a way that should c ...
Nonabelions in the fractional quantum hall effect
... The fractional quantum Hall effect (FQHE) [3], i.e. a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). ...
... The fractional quantum Hall effect (FQHE) [3], i.e. a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). ...
