Particle Creation in Inflationary Spacetime
... This section will quantize a free quantum field following [2]. For more information about quantum fields we also refer to [3]. Before this can be done we need to look at the dynamics of the field φa (~x, t). Classically dynamics in space could be determined with the Lagrangian, a function of the var ...
... This section will quantize a free quantum field following [2]. For more information about quantum fields we also refer to [3]. Before this can be done we need to look at the dynamics of the field φa (~x, t). Classically dynamics in space could be determined with the Lagrangian, a function of the var ...
Notes on Calculus II Integral Calculus Miguel A. Lerma
... The symbols at the left historically were intended to mean an infinite R sum, represented by a long “S” (the integral symbol ), of infinitely small amounts f (x) dx. The symbol dx was interpreted as the length of an “infinitesimal” interval, sort of what ∆x becomes for infinite n. This interpretatio ...
... The symbols at the left historically were intended to mean an infinite R sum, represented by a long “S” (the integral symbol ), of infinitely small amounts f (x) dx. The symbol dx was interpreted as the length of an “infinitesimal” interval, sort of what ∆x becomes for infinite n. This interpretatio ...
Lecture Notes of my Course on Quantum Computing
... P two standard assumptions for probability distributions are px ≥ 0 and x px = 1. Both the inputs and outputs to the circuits are random vectors. Circuits naturally act on probability distributions, and this is an example of a push-forward measure. We, however, will need a matrix representation of t ...
... P two standard assumptions for probability distributions are px ≥ 0 and x px = 1. Both the inputs and outputs to the circuits are random vectors. Circuits naturally act on probability distributions, and this is an example of a push-forward measure. We, however, will need a matrix representation of t ...
Evolution without evolution: Dynamics described by stationary
... block-diagonal density matrix in which all terms connecting states of different energy are set equal to zero. The expectation values of all operators have no dependence on t for this density matrix, so it represents a stationary state. As a result, all of the observable clock-time dependence of any ...
... block-diagonal density matrix in which all terms connecting states of different energy are set equal to zero. The expectation values of all operators have no dependence on t for this density matrix, so it represents a stationary state. As a result, all of the observable clock-time dependence of any ...
master equation for state occupancies of an open quantum system 121
... the CQS. Transitions between the ath and the bth states are associated with the off-diagonal transfer operator V . To generalize a situation, we suppose that the position of CQS energy levels can be alternated by regular ac-fields or non-regular stochastic fields so that the energy of the ath state ...
... the CQS. Transitions between the ath and the bth states are associated with the off-diagonal transfer operator V . To generalize a situation, we suppose that the position of CQS energy levels can be alternated by regular ac-fields or non-regular stochastic fields so that the energy of the ath state ...
Superconducting Circuits and Quantum Computation
... The basic component of a quantum computer is the qubit, the quantum analog to today’s bits. Any two-level quantum system could serve as a qubit; however, the qubit must satisfy two major criteria for practical quantum computing: long coherence times and the ability to scale to thousands of qubits. P ...
... The basic component of a quantum computer is the qubit, the quantum analog to today’s bits. Any two-level quantum system could serve as a qubit; however, the qubit must satisfy two major criteria for practical quantum computing: long coherence times and the ability to scale to thousands of qubits. P ...
Perches, Post-holes and Grids
... group the coordinates (manually again) according to the buildings to which the corresponding corner post-holes belong. The next step is statistical, namely to undertake a quantogram analysis based on individual building widths and depths after the manner of the investigation of the Huggins et al (19 ...
... group the coordinates (manually again) according to the buildings to which the corresponding corner post-holes belong. The next step is statistical, namely to undertake a quantogram analysis based on individual building widths and depths after the manner of the investigation of the Huggins et al (19 ...
Thermodynamics of the high temperature Quark-Gluon - IPhT
... are coming from lattice gauge calculations (for recent reviews see e.g. Refs. [1, 2]). These are at present the unique tools allowing a detailed study of the transition region where various interesting phenomena are taking place, such as colour deconfinement or chiral symmetry restoration. In these ...
... are coming from lattice gauge calculations (for recent reviews see e.g. Refs. [1, 2]). These are at present the unique tools allowing a detailed study of the transition region where various interesting phenomena are taking place, such as colour deconfinement or chiral symmetry restoration. In these ...
From Quantum theory to Quantum theology: Abstract J
... Max Planck's quantum hypothesis4 was the first indication that the inexorable determinism of classic3I physics had to be abandoned. Again, the implications of this hypothesis were not realised until 1926 when Werner Heisenberg formulated his famous uncertainty principleS. Particles no longer had sep ...
... Max Planck's quantum hypothesis4 was the first indication that the inexorable determinism of classic3I physics had to be abandoned. Again, the implications of this hypothesis were not realised until 1926 when Werner Heisenberg formulated his famous uncertainty principleS. Particles no longer had sep ...
Quantum Expanders: Motivation and Constructions
... The algebraic definition of expansion views a regular graph G = (V, E) as a linear operator on a Hilbert space V of dimension |V |. In this view an element v ∈ V is identified with a basis vector |vi ∈ V, and a distribution π on V corresponds to the vector |πi = ∑v∈V π(v) |vi. The action of G on V i ...
... The algebraic definition of expansion views a regular graph G = (V, E) as a linear operator on a Hilbert space V of dimension |V |. In this view an element v ∈ V is identified with a basis vector |vi ∈ V, and a distribution π on V corresponds to the vector |πi = ∑v∈V π(v) |vi. The action of G on V i ...
2 - Introduction of a Quantum of Time ("chronon"), and its
... many serious problems except when the field of the particle is neglected.4 By replacing Dirac’s differential equation with two finitedifference equations, Caldirola developed a theory in which the main difficulties of Dirac’s theory were overcome. As seen later, in Caldirola’s relativistically invar ...
... many serious problems except when the field of the particle is neglected.4 By replacing Dirac’s differential equation with two finitedifference equations, Caldirola developed a theory in which the main difficulties of Dirac’s theory were overcome. As seen later, in Caldirola’s relativistically invar ...
1 Correlated Electrons: Why we need Models to - cond
... One can probably find the Baym-Kadanoff interacting potential Φ[G] for simple lattice models using quantum Monte Carlo (QMC). Unfortunately, due to the sign problem in lattice simulations, this numerically exact solution of electronic correlation problem is not possible. On the other hand, one can o ...
... One can probably find the Baym-Kadanoff interacting potential Φ[G] for simple lattice models using quantum Monte Carlo (QMC). Unfortunately, due to the sign problem in lattice simulations, this numerically exact solution of electronic correlation problem is not possible. On the other hand, one can o ...
PHILOSOPHY OF QUANTUM INFORMATION
... Rohrlich and I discovered are just a stand-alone example, and in order for their meaning to be evaluated they need to be integrated into a full theory that will explain all the known phenomena, along with instances in which stronger-than quantum correlations would appear. While this is certainly tru ...
... Rohrlich and I discovered are just a stand-alone example, and in order for their meaning to be evaluated they need to be integrated into a full theory that will explain all the known phenomena, along with instances in which stronger-than quantum correlations would appear. While this is certainly tru ...
Shor`s Algorithm for Factorizing Large Integers
... where ζ = e2πi/q . If q is a product of small prime factors, then Uq can be factored as a product of a small number (polynomial in log(q)) of simpler unitary transformations, each representing the action of a quantum gate acting on only one or two qubits. (E.g. if q = 2 then only ( + 1)/2 such ga ...
... where ζ = e2πi/q . If q is a product of small prime factors, then Uq can be factored as a product of a small number (polynomial in log(q)) of simpler unitary transformations, each representing the action of a quantum gate acting on only one or two qubits. (E.g. if q = 2 then only ( + 1)/2 such ga ...
PDF only - at www.arxiv.org.
... analysis of the standard theory in light of certain experimental results, with the purpose of understanding the precise relationship between a measured quantum system and its measuring device. The analysis concludes that this "entangled state," also known as t ...
... analysis of the standard theory in light of certain experimental results, with the purpose of understanding the precise relationship between a measured quantum system and its measuring device. The analysis concludes that this "entangled state," also known as t ...
Fast direct solvers for elliptic PDEs
... 3. Ãσ,τ is a submatrix of A for all σ, τ . Our choice leads to some loss of accuracy, but vastly simplifies the task of computing compressed representations in the context of integral equations. (For instance, if the original A represents a Nyström discretization, then the HSS representation on eac ...
... 3. Ãσ,τ is a submatrix of A for all σ, τ . Our choice leads to some loss of accuracy, but vastly simplifies the task of computing compressed representations in the context of integral equations. (For instance, if the original A represents a Nyström discretization, then the HSS representation on eac ...