Introduction to Integrable Models
... Allowed pairs are restricted to 0 ≤ λ̃1 ≤ λ̃2 ≤ L − 1. Switching λ̃1 with λ̃2 interchanges k1 and k2 and leads to the same solution. L( L + 1)/2 pairs meet the restriction, however only L( L − 1)/2 of them produce solutions, which corresponds to the size of the Hilbert space. There are three distinc ...
... Allowed pairs are restricted to 0 ≤ λ̃1 ≤ λ̃2 ≤ L − 1. Switching λ̃1 with λ̃2 interchanges k1 and k2 and leads to the same solution. L( L + 1)/2 pairs meet the restriction, however only L( L − 1)/2 of them produce solutions, which corresponds to the size of the Hilbert space. There are three distinc ...
Classical vs Quantum Information - UMD Math
... (probability distribution) can be represented in one and only one way as a mixture of extremal states, the vertices of the simplex. No other state space has this feature: if the state space is not a simplex, the representation of mixed states as convex combinations of extremal states is not unique. ...
... (probability distribution) can be represented in one and only one way as a mixture of extremal states, the vertices of the simplex. No other state space has this feature: if the state space is not a simplex, the representation of mixed states as convex combinations of extremal states is not unique. ...
Quantum Computation by Adiabatic Evolution Edward Farhi, Jeffrey Goldstone Sam Gutmann
... suppose the Hamiltonian (2.29) commutes with some operator, say for concreteness σx . This implies that a(s) = b(s) and d(s) = 0. Now for the two eigenvalues to be equal at some s we only require c to vanish at some s. As s varies from 0 to 1 it would not be surprising to find c(s) cross zero so we ...
... suppose the Hamiltonian (2.29) commutes with some operator, say for concreteness σx . This implies that a(s) = b(s) and d(s) = 0. Now for the two eigenvalues to be equal at some s we only require c to vanish at some s. As s varies from 0 to 1 it would not be surprising to find c(s) cross zero so we ...
Charged domain-wall dynamics in doped antiferromagnets and spin
... cuprates.17 If the domain-wall lattice is in a disordered state as sketched in Fig. 2, the Bragg peaks will broaden in momentum space with a width inversely proportional to the correlation length of the domain-wall lattice. Moreover, because the ~1,0! and ~0,1! directions are equivalent, the incomme ...
... cuprates.17 If the domain-wall lattice is in a disordered state as sketched in Fig. 2, the Bragg peaks will broaden in momentum space with a width inversely proportional to the correlation length of the domain-wall lattice. Moreover, because the ~1,0! and ~0,1! directions are equivalent, the incomme ...
A conformal field theory approach to the fractional quantum Hall
... called the fusion of the particles and it obeys certain fusion rules, φa × φb = ...
... called the fusion of the particles and it obeys certain fusion rules, φa × φb = ...
Syllabys for BSc(Major):
... Paper Code: PHYM 10100 Paper Name: Mechanics and Properties of matter Total Marks: 80 Total No. of Lectures: 50 Unit I: Newtonian Mechanics (No. of Lectures: 15)(Marks:25) Concept of frame of references (inertial and non inertial), transformation of space and time in Galilean Relativity, two-body pr ...
... Paper Code: PHYM 10100 Paper Name: Mechanics and Properties of matter Total Marks: 80 Total No. of Lectures: 50 Unit I: Newtonian Mechanics (No. of Lectures: 15)(Marks:25) Concept of frame of references (inertial and non inertial), transformation of space and time in Galilean Relativity, two-body pr ...
full text
... Action-angle variables play a central role in the description and analysis of internal dynamics of atomic and molecular systems. Such systems often have important integrable approximations for which these variables can be introduced. Particularly many approximations are obtained for the limit of sma ...
... Action-angle variables play a central role in the description and analysis of internal dynamics of atomic and molecular systems. Such systems often have important integrable approximations for which these variables can be introduced. Particularly many approximations are obtained for the limit of sma ...
Reflections on the four facets of symmetry: how physics
... symmetry revitalises and clarifies the long-standing philosophical debate between realists and their opponents. The notions of “reality”, “being”, “existence” or even “self” have always been tricky because one cannot define them without introducing some tautology. In the endless controversial discussi ...
... symmetry revitalises and clarifies the long-standing philosophical debate between realists and their opponents. The notions of “reality”, “being”, “existence” or even “self” have always been tricky because one cannot define them without introducing some tautology. In the endless controversial discussi ...
Baryons in O (4) and Vibron Model
... It is the goal of this paper to develop a constituent model for baryons that explains the observed clustering in the spectra of the light unflavored baryons. The paper is organized as follows. In Section II we motivate legitimacy of fundamental fields of specified mass and unspecified spin as they e ...
... It is the goal of this paper to develop a constituent model for baryons that explains the observed clustering in the spectra of the light unflavored baryons. The paper is organized as follows. In Section II we motivate legitimacy of fundamental fields of specified mass and unspecified spin as they e ...
Creating arbitrary quantum vibrational states in a carbon nanotube
... qubits [7,8] and consists of the following steps. Two-electron spin states split by a magnetic field are defined as our qubit. The qubit flip, the qubit-phonon swap, and the phase operations are applied alternately to obtain an arbitrary quantum vibration state of the CNT. The qubit is flipped from ...
... qubits [7,8] and consists of the following steps. Two-electron spin states split by a magnetic field are defined as our qubit. The qubit flip, the qubit-phonon swap, and the phase operations are applied alternately to obtain an arbitrary quantum vibration state of the CNT. The qubit is flipped from ...
Quantum Measurement and Control
... guarantees that there is at least one state of complete knowledge (that is, one configuration) that all observers agree is a possible state. We now consider measurement of a classical system. With a perfect measurement of X, the observer would simply find out its value, say x . The system state wo ...
... guarantees that there is at least one state of complete knowledge (that is, one configuration) that all observers agree is a possible state. We now consider measurement of a classical system. With a perfect measurement of X, the observer would simply find out its value, say x . The system state wo ...
Bell's theorem
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Bell's theorem is a ‘no-go theorem’ that draws an important distinction between quantum mechanics (QM) and the world as described by classical mechanics. This theorem is named after John Stewart Bell.In its simplest form, Bell's theorem states:Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from ""indifference"" to ""wild extravagance"". Lawrence Berkeley particle physicist Henry Stapp declared: ""Bell's theorem is the most profound discovery of science.""Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables). Bell concluded:Bell summarized one of the least popular ways to address the theorem, superdeterminism, in a 1985 BBC Radio interview: