Lectures on Thermodynamics and Statistical Mechanics
... where N denotes the number of molecules of the gas and k is a constant, known as Boltzmann’s constant. Another way of writing this is as follows. We define the Avogadro number as 6.02214 × 1023 . This number comes about as follows. The mass of an atom is primarily due to the protons and neutrons in ...
... where N denotes the number of molecules of the gas and k is a constant, known as Boltzmann’s constant. Another way of writing this is as follows. We define the Avogadro number as 6.02214 × 1023 . This number comes about as follows. The mass of an atom is primarily due to the protons and neutrons in ...
Vol. 9, No. 1 (Winter 1996) - Mathematics and Statistics
... Figure 1. The Euler characteristic (EC) of a solid EC = 0; and the EC decreases by 1 for each extra hole is the number of vertices − edges + faces − polyhedra. (d, e); in (f) the central cube is missing so the solid is For a single polyhedron (a) or several joined together hollow, in which case the ...
... Figure 1. The Euler characteristic (EC) of a solid EC = 0; and the EC decreases by 1 for each extra hole is the number of vertices − edges + faces − polyhedra. (d, e); in (f) the central cube is missing so the solid is For a single polyhedron (a) or several joined together hollow, in which case the ...
Quantum Field Theory and Coalgebraic Logic in Theoretical
... Moreover, the category of Boolean algebras and the category of the Stone-spaces are dual to each other, in the sense that, given two Boolean algebras A, B, and the respective Stone-spaces S(A), S(B), to a continuous function from S(A) to S(B) it corresponds a monotone function from B to A . Afterwar ...
... Moreover, the category of Boolean algebras and the category of the Stone-spaces are dual to each other, in the sense that, given two Boolean algebras A, B, and the respective Stone-spaces S(A), S(B), to a continuous function from S(A) to S(B) it corresponds a monotone function from B to A . Afterwar ...
On the Quantum Theory of Line–spectra
... for the temperature radiation which apart from an undetermined constant factor coincides with Planck’s, if we only assume that the frequency corresponding to the transition between the two states is determined by (1). If will therefore be seen that by reversing the line of argument, Einstein’s theor ...
... for the temperature radiation which apart from an undetermined constant factor coincides with Planck’s, if we only assume that the frequency corresponding to the transition between the two states is determined by (1). If will therefore be seen that by reversing the line of argument, Einstein’s theor ...
Optimal Inequalities for State-Independent Contextuality Linköping University Post Print
... The set of all (contextual as well as noncontextual) correlations for such a scenario can be represented by the following standard construction. We first use that, if Ak and A‘ are compatible, then the expectation value of Ak is not changed whether or not A‘ is measured in the same context. Thus, in ...
... The set of all (contextual as well as noncontextual) correlations for such a scenario can be represented by the following standard construction. We first use that, if Ak and A‘ are compatible, then the expectation value of Ak is not changed whether or not A‘ is measured in the same context. Thus, in ...
Quantum Mechanics Made Simple: Lecture Notes
... time, it is bizarre. The reason is that quantum mechanics is quite different from classical physics. The development of quantum mechanics is likened to watching two players having a game of chess, but the watchers have not a clue as to what the rules of the game are. By observations, and conjectures ...
... time, it is bizarre. The reason is that quantum mechanics is quite different from classical physics. The development of quantum mechanics is likened to watching two players having a game of chess, but the watchers have not a clue as to what the rules of the game are. By observations, and conjectures ...
Department of Physics, Chemistry and Biology Master’s Thesis
... In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer. In our efforts to ...
... In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer. In our efforts to ...
The Equivalence Myth of Quantum Mechanics
... To axiomatize a theory is to de$ne a set-theoretical predicate Patrick Suppes (1957, p. 249). The author endeavours to show two things: first, that Schriidinger’s (and Eckart’s) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and ...
... To axiomatize a theory is to de$ne a set-theoretical predicate Patrick Suppes (1957, p. 249). The author endeavours to show two things: first, that Schriidinger’s (and Eckart’s) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and ...
Quantum collision theory with phase-space distributions
... the use of quantum-mechanical phase-space distributions for the formulation and solution of scattering and production problems. These distributions, which are quantum generalizations of Boltzmann's N-particle distribution fN(PtR" ... ,pNRN,t), provide an intuitive picture of complex collision proces ...
... the use of quantum-mechanical phase-space distributions for the formulation and solution of scattering and production problems. These distributions, which are quantum generalizations of Boltzmann's N-particle distribution fN(PtR" ... ,pNRN,t), provide an intuitive picture of complex collision proces ...
Do we really understand quantum mechanics?
... Schrödinger, who soon started to work on this program; he successfully and rapidly completed it by proposing the equation which now bears his name, one of the most basic equations of all physics. Amusingly, Debye himself does not seem to have remembered the event. The anecdote may not be accurate; ...
... Schrödinger, who soon started to work on this program; he successfully and rapidly completed it by proposing the equation which now bears his name, one of the most basic equations of all physics. Amusingly, Debye himself does not seem to have remembered the event. The anecdote may not be accurate; ...
QuRE: The Quantum Resource Estimator Toolbox
... Quantum states can be also measured in the X and Z basis, and the measurement will be denoted by MX(m) and MZ(m) or the symbol of a measurement. Qubit initialization is denoted by P|0i(m) and P|+i(m) . The symbol EC (m) represents error correction that repairs encoded state. Most operations on state ...
... Quantum states can be also measured in the X and Z basis, and the measurement will be denoted by MX(m) and MZ(m) or the symbol of a measurement. Qubit initialization is denoted by P|0i(m) and P|+i(m) . The symbol EC (m) represents error correction that repairs encoded state. Most operations on state ...
PDF only - at www.arxiv.org.
... (although the term “wave mechanics” is now almost not used; it appears that it better reflects the essence of this theory compared with the traditional term “quantum mechanics”), in which the basis, de Broglie’s hypothesis (1924), argues that each electron has a wave-like behaviour and its correspon ...
... (although the term “wave mechanics” is now almost not used; it appears that it better reflects the essence of this theory compared with the traditional term “quantum mechanics”), in which the basis, de Broglie’s hypothesis (1924), argues that each electron has a wave-like behaviour and its correspon ...
A low-resource quantum factoring algorithm
... md + cd−1 md−1 + · · · + c1 m + c0 where each of cd−1 , . . . , c1 , c0 is between 0 and m − 1. Define f = X d + cd−1 X d−1 + · · · + c1 X + c0 ∈ Z[X], so that f (m) = N . Check whether f is irreducible; if not then the factorization of f immediately reveals a nontrivial factorization of N , as note ...
... md + cd−1 md−1 + · · · + c1 m + c0 where each of cd−1 , . . . , c1 , c0 is between 0 and m − 1. Define f = X d + cd−1 X d−1 + · · · + c1 X + c0 ∈ Z[X], so that f (m) = N . Check whether f is irreducible; if not then the factorization of f immediately reveals a nontrivial factorization of N , as note ...
Renormalization of the Drude Conductivity by the Electron-Phonon Interaction
... the renormalization of the resistivity is significant, the Bloch-Gruneisen term prevails already for temperatures from 10 K (see Ref. [17]). In the interval from helium to the Debye temperature the change of the renormalization term is of the order of lr0 , while the change of the Bloch-Gruneisen te ...
... the renormalization of the resistivity is significant, the Bloch-Gruneisen term prevails already for temperatures from 10 K (see Ref. [17]). In the interval from helium to the Debye temperature the change of the renormalization term is of the order of lr0 , while the change of the Bloch-Gruneisen te ...
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.