Analytic structure and power-series expansion of the S. A. Rakityansky
... points and is a single-valued analytic function of the energy E ∼ k 2 , and therefore can be expanded in a convergent series R(E) = a0 + a1 E + a2 E 2 + · · · , which is given by Eq. (1). From this reasoning a next logical step immediately follows: the function R(E) can be expanded in a more general ...
... points and is a single-valued analytic function of the energy E ∼ k 2 , and therefore can be expanded in a convergent series R(E) = a0 + a1 E + a2 E 2 + · · · , which is given by Eq. (1). From this reasoning a next logical step immediately follows: the function R(E) can be expanded in a more general ...
Chapter 38 - Quantum scattering
... Furthermore, in both versions of the Krein-Friedel-Lloyd formulas the energy argument E + iη can be replaced by the wavenumber argument k + iη′ . These expressions only make sense for wavenumbers on or above the real k-axis. In particular, if k is chosen to be real, η′ must be greater than zero. Oth ...
... Furthermore, in both versions of the Krein-Friedel-Lloyd formulas the energy argument E + iη can be replaced by the wavenumber argument k + iη′ . These expressions only make sense for wavenumbers on or above the real k-axis. In particular, if k is chosen to be real, η′ must be greater than zero. Oth ...
Entanglement spectrum of a random partition: Connection with the
... We will refer to this special point η = 0 as the Kitaev limit of the Hamiltonian (2), which proves to be a useful starting point for our analysis below. Let |(η) be the ground state of the Kitaev Hamiltonian with parameter |η| < 1 in the topological regime. Applying the random partitioning procedu ...
... We will refer to this special point η = 0 as the Kitaev limit of the Hamiltonian (2), which proves to be a useful starting point for our analysis below. Let |(η) be the ground state of the Kitaev Hamiltonian with parameter |η| < 1 in the topological regime. Applying the random partitioning procedu ...
Qubit metrology for building a fault-tolerant quantum
... can vary in amplitude, duration and frequency. More fundamentally, the Heisenberg uncertainty principle states that it is impossible to directly stabilise a single qubit as any measurement of a bit-flip error will produce a random flip in phase. The key to quantum error correction is measuring qubit p ...
... can vary in amplitude, duration and frequency. More fundamentally, the Heisenberg uncertainty principle states that it is impossible to directly stabilise a single qubit as any measurement of a bit-flip error will produce a random flip in phase. The key to quantum error correction is measuring qubit p ...
Quantum scattering
... quantization. For large R, the dominant behavior is given by the size of the circular enclosure with a correction in terms of the derivative of the scattering phase shift, approximation accurate to order 1/R. However, not all is well: the area under consideration tends to infinity. We regularize thi ...
... quantization. For large R, the dominant behavior is given by the size of the circular enclosure with a correction in terms of the derivative of the scattering phase shift, approximation accurate to order 1/R. However, not all is well: the area under consideration tends to infinity. We regularize thi ...
Harmony of Scattering Amplitudes: From gauge theory
... means integrals are badly behaved in the UV Much more sophisticated power counting in supersymmetric theories but this is the basic idea. Reasons to focus on N = 8 maximal supergravity: Cremmer and Julia • With more susy suspect better UV properties. • High symmetry implies simplicity. Much simpler ...
... means integrals are badly behaved in the UV Much more sophisticated power counting in supersymmetric theories but this is the basic idea. Reasons to focus on N = 8 maximal supergravity: Cremmer and Julia • With more susy suspect better UV properties. • High symmetry implies simplicity. Much simpler ...
Strong Transient Modulation of Horizon Radiation
... an Unruh process to occur, i.e., for an accelerated detector that starts in the ground state (i.e., ∆E > 0) to get excited in the Minkowski vacuum. This amplitude can be nonzero because of the mathematical phenomenon that a wave that monotonically changes its frequency within a certain (e.g., negati ...
... an Unruh process to occur, i.e., for an accelerated detector that starts in the ground state (i.e., ∆E > 0) to get excited in the Minkowski vacuum. This amplitude can be nonzero because of the mathematical phenomenon that a wave that monotonically changes its frequency within a certain (e.g., negati ...
History of Quantum Mechanics or the Comedy of Errors1 Jean
... (complex valued) function defined on R3 : Ψ(x) ∈ C, x ∈ R3 . Its meaning, in quantum mechanics textbooks is that the square of its absolute value, |Ψ(x)|2 , gives the probability density of finding the particle at a given point, if one “measures” the particle’s position. A naive interpretation of th ...
... (complex valued) function defined on R3 : Ψ(x) ∈ C, x ∈ R3 . Its meaning, in quantum mechanics textbooks is that the square of its absolute value, |Ψ(x)|2 , gives the probability density of finding the particle at a given point, if one “measures” the particle’s position. A naive interpretation of th ...
98, 010506 (2007)
... tantalizingly close to fruition in these systems. Since the atoms are in identical spin states, s-wave scattering is Pauli prohibited and a p-wave resonance dominates, allowing the tunability of the atom-atom interaction in L 1 channel. Recently, it has been theoretically shown [12,13] that such i ...
... tantalizingly close to fruition in these systems. Since the atoms are in identical spin states, s-wave scattering is Pauli prohibited and a p-wave resonance dominates, allowing the tunability of the atom-atom interaction in L 1 channel. Recently, it has been theoretically shown [12,13] that such i ...
The role of quantum physics in the theory of subjective
... new quantum approach to consciousness, based on the consistent histories interpretation of quantum theory, which overcomes difficulties that have beset previous quantum approaches, illustrating this with a possible implementation of the idea of coherence. I shall first briefly review both the attrac ...
... new quantum approach to consciousness, based on the consistent histories interpretation of quantum theory, which overcomes difficulties that have beset previous quantum approaches, illustrating this with a possible implementation of the idea of coherence. I shall first briefly review both the attrac ...
Particle Spin and the Stern
... half integer values for the spin quantum number s in addition to the integer values. This theoretical result is confirmed by experiment. In nature there exist elementary particles for which s = 21 , 32 , 52 . . . such as the electron, proton, neutron, quark (all of which have spin s = 12 ), and more ...
... half integer values for the spin quantum number s in addition to the integer values. This theoretical result is confirmed by experiment. In nature there exist elementary particles for which s = 21 , 32 , 52 . . . such as the electron, proton, neutron, quark (all of which have spin s = 12 ), and more ...
A Quantum Rosetta Stone for Interferometry
... The result is a bit flip in the initial, computational, basis {|0i, |1i}, and this is readily measured. We call the formal analogy between these three systems the quantum Rosetta stone. The importance of the Rosetta stone was that, by giving an example of writing in three different languages: Greek, ...
... The result is a bit flip in the initial, computational, basis {|0i, |1i}, and this is readily measured. We call the formal analogy between these three systems the quantum Rosetta stone. The importance of the Rosetta stone was that, by giving an example of writing in three different languages: Greek, ...
LETTERS Generation of Fock states in a superconducting quantum circuit
... the one obtained from the splitting in Fig. 1. Both deviations can be explained by our having used an ‘on’ operating point slightly detuned from the minimal splitting in Fig. 1b, yielding slightly higher oscillation frequencies. The oscillation frequencies for higher photon number states, however, a ...
... the one obtained from the splitting in Fig. 1. Both deviations can be explained by our having used an ‘on’ operating point slightly detuned from the minimal splitting in Fig. 1b, yielding slightly higher oscillation frequencies. The oscillation frequencies for higher photon number states, however, a ...
High performance quantum computing
... ries information related to the quantum algorithm being run on the client side. As the photon stream transmitted to the client is the 3D topological lattice generated by the mainframe, interrogation of the quantum channel is unnecessary as the state transmitted is globally known. Additionally, the o ...
... ries information related to the quantum algorithm being run on the client side. As the photon stream transmitted to the client is the 3D topological lattice generated by the mainframe, interrogation of the quantum channel is unnecessary as the state transmitted is globally known. Additionally, the o ...
The additivity problem in quantum information theory
... memoryless quantum channels with respect to entangled encodings. Should the additivity fail, this would mean that applying entangled inputs to several independent uses of a quantum channel may result in superadditive increase of its capacity for transmission of classical information. However so far ...
... memoryless quantum channels with respect to entangled encodings. Should the additivity fail, this would mean that applying entangled inputs to several independent uses of a quantum channel may result in superadditive increase of its capacity for transmission of classical information. However so far ...
A statistical mechanics approach to the factorization problem
... very challenging to solve, and there is no known general solution. However, in the limit of very broadly distributed coupling constants Jij finding the ground state of this model maps to a minimum spanning tree problem, solvable by a greedy algorithm.8,9 The criterion is that the magnitude of each c ...
... very challenging to solve, and there is no known general solution. However, in the limit of very broadly distributed coupling constants Jij finding the ground state of this model maps to a minimum spanning tree problem, solvable by a greedy algorithm.8,9 The criterion is that the magnitude of each c ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.