Quantum Field Theory and Representation Theory
... Schrodinger’s equation: H is the generator of a unitary representation of the group R of time translations. Physical system has a Lie group G of symmetries → the Hilbert space of states H carries a unitary representation ρ of G. This representation may only be projective (up to complex phase), since ...
... Schrodinger’s equation: H is the generator of a unitary representation of the group R of time translations. Physical system has a Lie group G of symmetries → the Hilbert space of states H carries a unitary representation ρ of G. This representation may only be projective (up to complex phase), since ...
Closed timelike curves make quantum and classical computing equivalent
... computational resources, and would also make quantum and classical computers equivalent to each other in their computational power. Our results treat CTCs using the ‘causal consistency’ framework of Deutsch (1991), together with the assumption that a CTC involving polynomially many bits can be maint ...
... computational resources, and would also make quantum and classical computers equivalent to each other in their computational power. Our results treat CTCs using the ‘causal consistency’ framework of Deutsch (1991), together with the assumption that a CTC involving polynomially many bits can be maint ...
Heisenberg Groups and Noncommutative Fluxes
... the Deligne-Cheeger-Simons differential cohomology theory. We describe the structure of the groups, and give a heuristic explanation of Poincaré duality. Section 3 addresses generalized Maxwell theories. We carefully define electric and magnetic flux sectors and explain the role of Heisenberg group ...
... the Deligne-Cheeger-Simons differential cohomology theory. We describe the structure of the groups, and give a heuristic explanation of Poincaré duality. Section 3 addresses generalized Maxwell theories. We carefully define electric and magnetic flux sectors and explain the role of Heisenberg group ...
Three Quantum Algorithms to Solve 3-SAT
... n–registers can be represented as order 2n square matrices of complex entries. Usually (but not in this paper) such operators, as well as the corresponding matrices, are required to be unitary. In particular, this implies that the implemented operations are logically reversible (an operation is logi ...
... n–registers can be represented as order 2n square matrices of complex entries. Usually (but not in this paper) such operators, as well as the corresponding matrices, are required to be unitary. In particular, this implies that the implemented operations are logically reversible (an operation is logi ...
Parallel Universes Is there a copy of you Not just a staple
... But recent observations of the three-dimensional galaxy distribution and the microwave background have shown that the arrangement of matter gives way to dull uniformity on large scales, with no coherent structures larger than about 1024 meters. Assuming that this pattern continues, space beyond our ...
... But recent observations of the three-dimensional galaxy distribution and the microwave background have shown that the arrangement of matter gives way to dull uniformity on large scales, with no coherent structures larger than about 1024 meters. Assuming that this pattern continues, space beyond our ...
Commutation relations for functions of operators
... where the 共 ⬘兲 symbol denotes differentiation with respect to the variable. The derivation of Eqs. 共6兲 and 共7兲 is a typical and almost obligatory exercise in a modern text on quantum mechanics. The standard way of proceeding is to consider the commutator of x with increasing powers of p, to use indu ...
... where the 共 ⬘兲 symbol denotes differentiation with respect to the variable. The derivation of Eqs. 共6兲 and 共7兲 is a typical and almost obligatory exercise in a modern text on quantum mechanics. The standard way of proceeding is to consider the commutator of x with increasing powers of p, to use indu ...
Quantum Field Theory on Curved Backgrounds. I
... Then Γ (ψn ) → Γ (ψ) in the strong operator topology on B(E). The proof of theorem 1.1 follows standard arguments in analysis. Let us give a sense of how it is to be used. If all the elements of a certain one-parameter group of isometries ψt are such that Γ (ψt ) have bounded quantizations, then t → ...
... Then Γ (ψn ) → Γ (ψ) in the strong operator topology on B(E). The proof of theorem 1.1 follows standard arguments in analysis. Let us give a sense of how it is to be used. If all the elements of a certain one-parameter group of isometries ψt are such that Γ (ψt ) have bounded quantizations, then t → ...
Long Distance, Unconditional Teleportation of Atomic States V 87, N
... cavities, with their respective atoms either physically displaced or optically detuned so that no A-to-B absorptions occur. After a short loading interval (a few cold-cavity lifetimes, say, 400 ns), each atom is moved (or tuned) into the absorbing position and B-to-D pumping is initiated. After abou ...
... cavities, with their respective atoms either physically displaced or optically detuned so that no A-to-B absorptions occur. After a short loading interval (a few cold-cavity lifetimes, say, 400 ns), each atom is moved (or tuned) into the absorbing position and B-to-D pumping is initiated. After abou ...
Quantum Spin Hall Effect and their Topological Design of Devices
... For other way, the spin effects in their chirality and helically could to bring the step of one case in other under change of the regime, let magnetic field or magnetization or nothing of the two. However, the manager of spin is not easy, if we not have some topological considerations to the manager ...
... For other way, the spin effects in their chirality and helically could to bring the step of one case in other under change of the regime, let magnetic field or magnetization or nothing of the two. However, the manager of spin is not easy, if we not have some topological considerations to the manager ...
Ultimate Intelligence Part I: Physical Completeness and Objectivity
... would be referring to halting oracles, which would be truly incomputable, and by our arguments in this paper, have no physical relevance. Note that the halting probability is semi-computable. The computable pdf model is a good abstraction of the observations in quantum mechanics (QM). In QM, the wav ...
... would be referring to halting oracles, which would be truly incomputable, and by our arguments in this paper, have no physical relevance. Note that the halting probability is semi-computable. The computable pdf model is a good abstraction of the observations in quantum mechanics (QM). In QM, the wav ...
The harmonic oscillator in quantum mechanics: A third way F. Marsiglio
... potential alone, because the wave function will be sufficiently restricted to the central region of the harmonic oscillator potential so that it will not “feel” the walls of the infinite square well. High energy states will not be well described by the harmonic oscillator results, because they will ...
... potential alone, because the wave function will be sufficiently restricted to the central region of the harmonic oscillator potential so that it will not “feel” the walls of the infinite square well. High energy states will not be well described by the harmonic oscillator results, because they will ...
Extremal eigenvalues of local Hamiltonians
... that product states nearly match the energy of some other state (e.g. the true ground state) with possibly unknown energy while our paper puts explicit bounds on the maximum and/or minimum energy. ...
... that product states nearly match the energy of some other state (e.g. the true ground state) with possibly unknown energy while our paper puts explicit bounds on the maximum and/or minimum energy. ...
Quantum State Transfer via Noisy Photonic and Phononic Waveguides
... i.e., the operator of the first cavity mode at initial time ti is mapped to the second cavity mode at final time tf , with no admixture from bR ðtÞ [26]. In other words, an arbitrary photon superposition state prepared initially in the first cavity can be faithfully transferred to the second distant ...
... i.e., the operator of the first cavity mode at initial time ti is mapped to the second cavity mode at final time tf , with no admixture from bR ðtÞ [26]. In other words, an arbitrary photon superposition state prepared initially in the first cavity can be faithfully transferred to the second distant ...
The Spectrum of the Hydrogen Atom
... • Paul Dirac did a lot of work in quantum mechanics and relativity, and proposed an equation of motion for an electron, taking into consideration relativistic effects. • Albert Einstein did a lot of work in order to explain the photoelectric effect, but did not like the path the new quantum mechanic ...
... • Paul Dirac did a lot of work in quantum mechanics and relativity, and proposed an equation of motion for an electron, taking into consideration relativistic effects. • Albert Einstein did a lot of work in order to explain the photoelectric effect, but did not like the path the new quantum mechanic ...
Quantum defect theory description of weakly bound levels and Feshbach...
... MQDT was born in atomic physics long ago, as a highly successful theory to explain the spectra of autoionizing states in complex atoms and the link between bound and continuum states of an outermost atomic electron [16–18]. Since those early developments, MQDT has been extended beyond the long-range ...
... MQDT was born in atomic physics long ago, as a highly successful theory to explain the spectra of autoionizing states in complex atoms and the link between bound and continuum states of an outermost atomic electron [16–18]. Since those early developments, MQDT has been extended beyond the long-range ...
Max Born
Max Born (German: [bɔɐ̯n]; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics for his ""fundamental research in Quantum Mechanics, especially in the statistical interpretation of the wave function"".Born was born in 1882 in Breslau, then in Germany, now in Poland and known as Wrocław. He entered the University of Göttingen in 1904, where he found the three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of ""Stability of Elastica in a Plane and Space"", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.In the First World War after originally being placed as a radio operator, due to his specialist knowledge he was moved to research duties regarding sound ranging. In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees under Born at Göttingen, and his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.In January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. He emigrated to Britain, where he took a job at St John's College, Cambridge, and wrote a popular science book, The Restless Universe, as well as Atomic Physics, which soon became a standard text book. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, where, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Max Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe. He remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany. He died in hospital in Göttingen on 5 January 1970.