Reconstruction on Wigner Functions on Different

... (let say q^ and p^ ) it is not possible to construct an eigenstate of these two operators, and therefore it is inevitable that the simultaneous measurement of two non-commuting observables introduces additional noise (of quantum origin) into measured data [5, 8, 9, 18, 19]. To describe a process of ...

... (let say q^ and p^ ) it is not possible to construct an eigenstate of these two operators, and therefore it is inevitable that the simultaneous measurement of two non-commuting observables introduces additional noise (of quantum origin) into measured data [5, 8, 9, 18, 19]. To describe a process of ...

Dirac Operators on Noncommutative Spacetimes ?

... of the classical Dirac operator, which at first seem equally well motivated and are not obviously equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac opera ...

... of the classical Dirac operator, which at first seem equally well motivated and are not obviously equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac opera ...

The de Broglie Wave as Evidence of a Deeper Wave Structure

... of the unobserved cat that is at once dead and alive (Schrödinger [12]). However, it has been assumed in quantum mechanics, both in its standard form and in its many reinterpretations, as it was by de Broglie and Schrödinger, that the de Broglie wave is a wave in its own right. How the de Broglie wa ...

... of the unobserved cat that is at once dead and alive (Schrödinger [12]). However, it has been assumed in quantum mechanics, both in its standard form and in its many reinterpretations, as it was by de Broglie and Schrödinger, that the de Broglie wave is a wave in its own right. How the de Broglie wa ...

11 Harmonic oscillator and angular momentum — via operator algebra

... a generalized angular momentum denoted by J. As mentioned in the introduction, it then turns out, firstly, that we are able to reproduce the results for orbital angular momenta, with integer quantum numbers l and m (see Tillegg 5 or 6.1 in Bransden & Joachain). Secondly, the algebraic method furnish ...

... a generalized angular momentum denoted by J. As mentioned in the introduction, it then turns out, firstly, that we are able to reproduce the results for orbital angular momenta, with integer quantum numbers l and m (see Tillegg 5 or 6.1 in Bransden & Joachain). Secondly, the algebraic method furnish ...

Gauge and Matter Fields on a Lattice - Generalizing

... not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the Toric Code (TC) introduced by A. Kitaev in ...

... not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the Toric Code (TC) introduced by A. Kitaev in ...

lecture notes - Analysis Group TU Delft

... theorem for unbounded selfadjoint operators in Hilbert spaces, and some applications to elementary quantum mechanics. The main focus will be on the decomposition of a selfadjoint operator onto its family of spectral projections. Some elements of functional calculus will also be given. We will start ...

... theorem for unbounded selfadjoint operators in Hilbert spaces, and some applications to elementary quantum mechanics. The main focus will be on the decomposition of a selfadjoint operator onto its family of spectral projections. Some elements of functional calculus will also be given. We will start ...

Bulk Locality and Quantum Error Correction in AdS/CFT arXiv

... mentioned in the introduction, that is that no nontrivial operator in the CFT can commute with all local CFT operators on Σ. To avoid this contradiction it must be the case that the representations of φ(x) in different wedges are not really all the same operator on the CFT Hilbert space. We can see ...

... mentioned in the introduction, that is that no nontrivial operator in the CFT can commute with all local CFT operators on Σ. To avoid this contradiction it must be the case that the representations of φ(x) in different wedges are not really all the same operator on the CFT Hilbert space. We can see ...

Axial gravity, massless fermions and trace anomalies

... diagram techniques, where the fermion path integral measure does not play a direct role. However there is a way to carry out the same calculation on a theory of Dirac fermions, so that no fastidious objections can be raised about the fermion functional integral measure. Here is where the axial metri ...

... diagram techniques, where the fermion path integral measure does not play a direct role. However there is a way to carry out the same calculation on a theory of Dirac fermions, so that no fastidious objections can be raised about the fermion functional integral measure. Here is where the axial metri ...

Implications of the two nodal domains conjecture for ground state

... R for which a wave function vanishes, i.e., (R) = 0. With R we indicate the collective coordinates of the N particles in D dimensions. The nodal set implicitly deﬁnes two or more nodal domains (sometimes called nodal cells or nodal pockets), i.e., a connected set of points bounded by the nodal set ...

... R for which a wave function vanishes, i.e., (R) = 0. With R we indicate the collective coordinates of the N particles in D dimensions. The nodal set implicitly deﬁnes two or more nodal domains (sometimes called nodal cells or nodal pockets), i.e., a connected set of points bounded by the nodal set ...

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... commutation relations in all generality, following from the properties of rotations. The specific case of orbital angular momentum L will be dealt with in a later set of notes. We have shown that the only way the unitary operators U can reproduce the multiplication law for the classical rotations R ...

... commutation relations in all generality, following from the properties of rotations. The specific case of orbital angular momentum L will be dealt with in a later set of notes. We have shown that the only way the unitary operators U can reproduce the multiplication law for the classical rotations R ...

Coherent State Wave Functions on the Torus

... charged quasi-particles[18], that do not obey the ordinary statistics of fermions or bosons. This new form of statistics constitutes a generalization of the fermion/boson statistics and can only be obtained in systems with lower dimensionality than 3. display non-abelian statistics[20], in theory. ...

... charged quasi-particles[18], that do not obey the ordinary statistics of fermions or bosons. This new form of statistics constitutes a generalization of the fermion/boson statistics and can only be obtained in systems with lower dimensionality than 3. display non-abelian statistics[20], in theory. ...

Indecomposable Representations of the Square

... the special case of Λ1 = Λ2 = 0 this requirement may be satisfied. Now, let us first consider R1±1 . Under the action of representations ρ̃ of R1±1 , any point (k10 , k20 ) in the lattice pattern of {F (k1 , k2 )} moves only along a ray with its started point (k10 , k20 ) and arrives at all the poin ...

... the special case of Λ1 = Λ2 = 0 this requirement may be satisfied. Now, let us first consider R1±1 . Under the action of representations ρ̃ of R1±1 , any point (k10 , k20 ) in the lattice pattern of {F (k1 , k2 )} moves only along a ray with its started point (k10 , k20 ) and arrives at all the poin ...

Many Body Quantum Mechanics

... C there is a unique ψ ∈ H such that Λ(φ) = (ψ, φ) for all φ ∈ H. We denote by H∗ the dual of the Hilbert space H, i.e., the space of all continuous linear functionals on H. The map J : H → H∗ defined by J(ψ)(φ) = (ψ, φ) is according to Riesz representation Theorem an anti-linear isomorphism. That J ...

... C there is a unique ψ ∈ H such that Λ(φ) = (ψ, φ) for all φ ∈ H. We denote by H∗ the dual of the Hilbert space H, i.e., the space of all continuous linear functionals on H. The map J : H → H∗ defined by J(ψ)(φ) = (ψ, φ) is according to Riesz representation Theorem an anti-linear isomorphism. That J ...

Irreducible Tensor Operators and the Wigner

... The Wigner-Eckart theorem concerns matrix elements of a type that is of frequent occurrence in all areas of quantum physics, especially in perturbation theory and in the theory of the emission and absorption of radiation. This theorem allows one to determine very quickly the selection rules for the ...

... The Wigner-Eckart theorem concerns matrix elements of a type that is of frequent occurrence in all areas of quantum physics, especially in perturbation theory and in the theory of the emission and absorption of radiation. This theorem allows one to determine very quickly the selection rules for the ...

Three problems from quantum optics

... of light, do not change their character when subject to a linear mode transformation at a beam splitter etc. Thanks to the so-called overcompleteness of the set of coherent states they can be employed even for describing situations in which coherent states themselves do not take part, and simplify c ...

... of light, do not change their character when subject to a linear mode transformation at a beam splitter etc. Thanks to the so-called overcompleteness of the set of coherent states they can be employed even for describing situations in which coherent states themselves do not take part, and simplify c ...

Relativistic quantum mechanics and the S matrix

... U(a,b) that represent these transformations are used to map the quantum mechanical state vectors of a system from one inertial frame to another. The unitary operators that represent the proper group can be constructed by exponentiation from a set of ten generators 兵 H,P,J,K其 . Here H is the Hamilton ...

... U(a,b) that represent these transformations are used to map the quantum mechanical state vectors of a system from one inertial frame to another. The unitary operators that represent the proper group can be constructed by exponentiation from a set of ten generators 兵 H,P,J,K其 . Here H is the Hamilton ...

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... Regular fermion basis We can count regular fermions We can pair Majoranas into regular fermions and measure them How to chose? Number of pairings: Overlap between states To observe the state of the system we need to “fuse” two Majoranas ...

... Regular fermion basis We can count regular fermions We can pair Majoranas into regular fermions and measure them How to chose? Number of pairings: Overlap between states To observe the state of the system we need to “fuse” two Majoranas ...

Indirect measurement

... half the time it performs unitary Û0 , and half the time Û1 . Such gates arise naturally in certain schemes for quantum computation (notably, the linear optical scheme of Knill, Laflamme and Milburn). We can also think of the Bell state measurement in quantum teleportation as performing a probabil ...

... half the time it performs unitary Û0 , and half the time Û1 . Such gates arise naturally in certain schemes for quantum computation (notably, the linear optical scheme of Knill, Laflamme and Milburn). We can also think of the Bell state measurement in quantum teleportation as performing a probabil ...