Higher-derivative Lagrangians, nonlocality, problems, and solutions
... more interesting and disturbing problems, with examples. A natural method of removing all the problems of higher derivatives is reviewed. This method of "perturbative constraints" is required for at least one class of higher-derivative theories those which are associated with nonlocality. Nonlocalit ...
... more interesting and disturbing problems, with examples. A natural method of removing all the problems of higher derivatives is reviewed. This method of "perturbative constraints" is required for at least one class of higher-derivative theories those which are associated with nonlocality. Nonlocalit ...
Temporal preconditioners for marching on-in
... fields is different). For the delayed incident field, the constant level is lower. It can be concluded that the initial value of the solution is directly related to the incident field at the first time step. Therefore, usually the delay of the incident field is chosen to be very large, which results ...
... fields is different). For the delayed incident field, the constant level is lower. It can be concluded that the initial value of the solution is directly related to the incident field at the first time step. Therefore, usually the delay of the incident field is chosen to be very large, which results ...
Symmetry Principles and Conservation Laws in Atomic and
... The constancy of the LRL vector is a conservation principle, and since the governing criterion involves dynamics (namely that the force must have a strict inverse square form), the associated symmetry is called `dynamical symmetry'. Sometimes, it is also called an `accidental' symmetry. This symmetr ...
... The constancy of the LRL vector is a conservation principle, and since the governing criterion involves dynamics (namely that the force must have a strict inverse square form), the associated symmetry is called `dynamical symmetry'. Sometimes, it is also called an `accidental' symmetry. This symmetr ...
The Equivalence Myth of Quantum Mechanics
... matrix-valued electromagnetic fields with non-commuting components or to reformulate ‘the MaxwelllLorentz equations’; on the contrary, wave mechanics meshes quite nicely with classical electrodynamics due to the presence of the charge densities in Prop,, E EF;,,,. Schrodinger declared (1926~; 1927, ...
... matrix-valued electromagnetic fields with non-commuting components or to reformulate ‘the MaxwelllLorentz equations’; on the contrary, wave mechanics meshes quite nicely with classical electrodynamics due to the presence of the charge densities in Prop,, E EF;,,,. Schrodinger declared (1926~; 1927, ...
Quantum One-Way Communication is Exponentially Stronger Than
... However, although Raz’s function can be computed using only O(log n) qubits, it seems to require at least two rounds of communication between Alice and Bob. This naturally leads to the following fundamental question, which has been open ever since Raz’s paper: can a similar exponential separation be ...
... However, although Raz’s function can be computed using only O(log n) qubits, it seems to require at least two rounds of communication between Alice and Bob. This naturally leads to the following fundamental question, which has been open ever since Raz’s paper: can a similar exponential separation be ...
Quantum mechanical modeling of the CNOT (XOR) gate
... To this end, for an isolated quantum (”microscopic”) system it is practicaly a matter of principle that its Hamiltonian has at least one group of the global symmetry. [E.g., for an EPR pair, there is the full (e.g., rotational) symmetry of the ”pair”. In the collission processes it is both theoretic ...
... To this end, for an isolated quantum (”microscopic”) system it is practicaly a matter of principle that its Hamiltonian has at least one group of the global symmetry. [E.g., for an EPR pair, there is the full (e.g., rotational) symmetry of the ”pair”. In the collission processes it is both theoretic ...
9. Orbits in stationary Potentials We have seen how to calculate
... Conclusion: the orbits do not occupy a 3 dimensional space in the 4-dimensional phase-space, but they occopy only a 2-dimensional space ! This indicates that there is an additional integral of motion: ’a non-classical integral’ The non-classical integral, plus the regular ’Energy’, constrain the orb ...
... Conclusion: the orbits do not occupy a 3 dimensional space in the 4-dimensional phase-space, but they occopy only a 2-dimensional space ! This indicates that there is an additional integral of motion: ’a non-classical integral’ The non-classical integral, plus the regular ’Energy’, constrain the orb ...
Ergodic Semigroups of Positivity Preserving Self
... Glimm and Jaffe [4] that the semigroup generated by the Hamiltonian is ergodic (see also [lo, 111). For the free Hamiltonian in a finite number of degrees of freedom, it was known that the semigroup was positivity improving-it was, thus, natural to try to prove this in general. Of course, Theorem 1 ...
... Glimm and Jaffe [4] that the semigroup generated by the Hamiltonian is ergodic (see also [lo, 111). For the free Hamiltonian in a finite number of degrees of freedom, it was known that the semigroup was positivity improving-it was, thus, natural to try to prove this in general. Of course, Theorem 1 ...
Supplementary notes on units
... The “trick” here was to write Coulomb’s Law without any constant of proportionality. This is the cgs algorithm for introducing new concepts into physics without introducing new units: Simply write down the law relating the new concept to already known quantities without a constant of proportionality ...
... The “trick” here was to write Coulomb’s Law without any constant of proportionality. This is the cgs algorithm for introducing new concepts into physics without introducing new units: Simply write down the law relating the new concept to already known quantities without a constant of proportionality ...
EXAMPLE 6 Find the gradient vector field of . Plot the gradient vector
... or, equivalently, by the vector equation r共t兲 苷 x共t兲 i y共t兲 j, and we assume that C is a smooth curve. [This means that r is continuous and r 共t兲 苷 0. See Section 10.2.] If we divide the parameter interval 关a, b兴 into n subintervals 关ti1, ti 兴 of equal width and we let x i 苷 x共ti 兲 and yi 苷 y共ti ...
... or, equivalently, by the vector equation r共t兲 苷 x共t兲 i y共t兲 j, and we assume that C is a smooth curve. [This means that r is continuous and r 共t兲 苷 0. See Section 10.2.] If we divide the parameter interval 关a, b兴 into n subintervals 关ti1, ti 兴 of equal width and we let x i 苷 x共ti 兲 and yi 苷 y共ti ...
Fidelity as a figure of merit in quantum error correction
... orthogonal space, it can be identified but not corrected. There are then two conceivable strategies: One is to apply some recovery operator Ri that effectively replaces the erroneous state with a predefined state. The other strategy is to discard the state and take note of the location of the error ...
... orthogonal space, it can be identified but not corrected. There are then two conceivable strategies: One is to apply some recovery operator Ri that effectively replaces the erroneous state with a predefined state. The other strategy is to discard the state and take note of the location of the error ...
