A model of interacting partons for hadronic structure functions
... In this inertial reference frame, the proton has a very large 3-momentum P and we may ignore its rest mass in comparison pµ = (|P|, P). The proton is thought of as consisting of several point-like constituents, the partons. The 4-momentum of a given parton is expressed as xpµ where 0 ≤ x ≤ 1 is the ...
... In this inertial reference frame, the proton has a very large 3-momentum P and we may ignore its rest mass in comparison pµ = (|P|, P). The proton is thought of as consisting of several point-like constituents, the partons. The 4-momentum of a given parton is expressed as xpµ where 0 ≤ x ≤ 1 is the ...
Approximate Quantum Error-Correcting Codes and Secret Sharing
... (verdict) qubit V which indicates acceptance or rejection. The classical basis states of V are called |acci, |reji by convention. For any fixed key k, we denote the corresponding super-operators by Ak and Vk . Bob may measure the qubit V to see whether or not the transmission was accepted or rejecte ...
... (verdict) qubit V which indicates acceptance or rejection. The classical basis states of V are called |acci, |reji by convention. For any fixed key k, we denote the corresponding super-operators by Ak and Vk . Bob may measure the qubit V to see whether or not the transmission was accepted or rejecte ...
Recurrence spectroscopy of atoms in electric fields: Scattering in the...
... for scattering into an orbit labeled by (k 8 ,n 8 ). In the isolated orbit limit the integrals in Eqs. ~22! and ~23! can be evaluated by stationary phase and they reduce to the primitive semiclassical scattering formula for a single scattering off the core, Eq. ~7! with J51. We can now write the sca ...
... for scattering into an orbit labeled by (k 8 ,n 8 ). In the isolated orbit limit the integrals in Eqs. ~22! and ~23! can be evaluated by stationary phase and they reduce to the primitive semiclassical scattering formula for a single scattering off the core, Eq. ~7! with J51. We can now write the sca ...
Nonlocal “realistic” Leggett models can be considered refuted by the
... measurements A and B are determined by the “preexisting” properties (hidden variables) the particles carry [1, 5]. However, the individual B outcomes cannot be considered to be predetermined by the polarization vectors v the photons B carry when they leave the source and the set of local hidden vari ...
... measurements A and B are determined by the “preexisting” properties (hidden variables) the particles carry [1, 5]. However, the individual B outcomes cannot be considered to be predetermined by the polarization vectors v the photons B carry when they leave the source and the set of local hidden vari ...
Relativistic dynamics, Green function and pseudodifferential operators
... operators (Hamiltonian, Lagrangian) in the field of relativistic theories has brought not only the problem of mathematical treatment of these non-local and nonlinear operators, but its physical interpretation also. The conceptual fact to find the physical interpretation of the square root operator ...
... operators (Hamiltonian, Lagrangian) in the field of relativistic theories has brought not only the problem of mathematical treatment of these non-local and nonlinear operators, but its physical interpretation also. The conceptual fact to find the physical interpretation of the square root operator ...
Experimental nonlocal and surreal Bohmian trajectories
... has no autonomous hidden variable assigned to it in standard Bohmian mechanics. [In some extensions to Bohmian mechanics, autonomous hidden variables are assigned to degrees of freedom other than position, such as spin (19). See Hiley and Callaghan (20) for a discussion in the context of the origina ...
... has no autonomous hidden variable assigned to it in standard Bohmian mechanics. [In some extensions to Bohmian mechanics, autonomous hidden variables are assigned to degrees of freedom other than position, such as spin (19). See Hiley and Callaghan (20) for a discussion in the context of the origina ...
GroupMeeting_pjlin_20040810_pomeron
... The Pomeron couples with the same strength to the proton and antiproton because the Pomeron carries the quantum numbers of the vacuum. The Regge trajectory can have different couplings to particles and antiparticles. This accounts for the difference between the p p and p p cross-sections at lo ...
... The Pomeron couples with the same strength to the proton and antiproton because the Pomeron carries the quantum numbers of the vacuum. The Regge trajectory can have different couplings to particles and antiparticles. This accounts for the difference between the p p and p p cross-sections at lo ...
Path integrals and the classical approximation
... We use W (~x, E) if we want to find an energy eigenfunction in the classical limit. For instance, we can think of a wave function that represents waves that start from a source at location ~x0 . If we move ~x0 to somewhere far away near the −z axis, then we would have waves that start as plane waves ...
... We use W (~x, E) if we want to find an energy eigenfunction in the classical limit. For instance, we can think of a wave function that represents waves that start from a source at location ~x0 . If we move ~x0 to somewhere far away near the −z axis, then we would have waves that start as plane waves ...
How Many Query Superpositions Are Needed to Learn?
... (or query complexity) required by exact learners. Our aim is to obtain lower and upper bounds on the query complexity that are valid under any choice of queries defining the learning game. According to the first goal, we introduce in Sect. 3 the quantum protocol concept, a notion that allows us to d ...
... (or query complexity) required by exact learners. Our aim is to obtain lower and upper bounds on the query complexity that are valid under any choice of queries defining the learning game. According to the first goal, we introduce in Sect. 3 the quantum protocol concept, a notion that allows us to d ...
Quantum Measurements with Dynamically Bistable Systems
... dropped the term −λ 2 QB ∂P3 ρ̄W /4 which comes from the operator L̂(2) in Eq. (11). One can show that, for typical |δ P| ∼ |η |1/2 , this term leads to corrections ∼ η , λ to ρ̄W . Eq. (20) has a standard form of the equation for classical diffusion in a potential U(δ P), with diffusion coefficient ...
... dropped the term −λ 2 QB ∂P3 ρ̄W /4 which comes from the operator L̂(2) in Eq. (11). One can show that, for typical |δ P| ∼ |η |1/2 , this term leads to corrections ∼ η , λ to ρ̄W . Eq. (20) has a standard form of the equation for classical diffusion in a potential U(δ P), with diffusion coefficient ...
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.