On the conundrum of deriving exact solutions from approximate
... beyond second-order vanish [54]. Since fmn(t) is linear in these variables, the same is true for the cumulants in Eq. (37) and, consequently, only the terms with ‘ = 1, 2 contribute to this expansion. Evaluating the expansion coefficients explicitly, one finds that they are identical to those of the se ...
... beyond second-order vanish [54]. Since fmn(t) is linear in these variables, the same is true for the cumulants in Eq. (37) and, consequently, only the terms with ‘ = 1, 2 contribute to this expansion. Evaluating the expansion coefficients explicitly, one finds that they are identical to those of the se ...
Angular Momentum and Central Forces
... A new operator L2 is introduced because, this operator commutes with each individual components of L, however the components of L does not commute with each other. L2 is given by, L =L +L +L When a measurement is made, we can find the total angular momentum and only one other component at a time. Fo ...
... A new operator L2 is introduced because, this operator commutes with each individual components of L, however the components of L does not commute with each other. L2 is given by, L =L +L +L When a measurement is made, we can find the total angular momentum and only one other component at a time. Fo ...
Full Text - University of Arizona
... The interference pattern of a set of intersecting laser beams can create a stable periodic potential for neutral atoms through the AC Stark shift (light shift), which can trap, and thereby organize atoms in an ordered, crystal-like structure. Historically, interest in these "optical lattices" grew o ...
... The interference pattern of a set of intersecting laser beams can create a stable periodic potential for neutral atoms through the AC Stark shift (light shift), which can trap, and thereby organize atoms in an ordered, crystal-like structure. Historically, interest in these "optical lattices" grew o ...
Particle Creation in Inflationary Spacetime
... Quantum mechanics combined with relativity violates the preservation of the number of particles in a system[2]. At very small scales particle anti-particle pairs can pop into existence. At any point in space, even empty space, these particle pairs can appear and disappear. In quantum mechanics we ha ...
... Quantum mechanics combined with relativity violates the preservation of the number of particles in a system[2]. At very small scales particle anti-particle pairs can pop into existence. At any point in space, even empty space, these particle pairs can appear and disappear. In quantum mechanics we ha ...
Realization of an Optomechanical Interface
... increasing lattice laser power, and measure !m =2 ¼ 244 kHz at P ¼ 76 mW. We attribute this to reduced tensile stress due to thermal expansion of the membrane, which is locally heated by the lattice laser [25]. The mechanical quality factor Q ¼ !m =m ¼ !m =2 of the fundamental mode is determined ...
... increasing lattice laser power, and measure !m =2 ¼ 244 kHz at P ¼ 76 mW. We attribute this to reduced tensile stress due to thermal expansion of the membrane, which is locally heated by the lattice laser [25]. The mechanical quality factor Q ¼ !m =m ¼ !m =2 of the fundamental mode is determined ...
Cloaking of Matter Waves
... shell is eliminated if a nonlinear radial scaling function gr is chosen such that g0 rjrr2 1, i.e. mr2 m0 and V2 0 at the outer shell of the cloak. Equations. (10) shows that mr2 approaches infinity at the inner shell of the cloak. This would not be possible in a realistic cloaking design ...
... shell is eliminated if a nonlinear radial scaling function gr is chosen such that g0 rjrr2 1, i.e. mr2 m0 and V2 0 at the outer shell of the cloak. Equations. (10) shows that mr2 approaches infinity at the inner shell of the cloak. This would not be possible in a realistic cloaking design ...
Position-Momentum Duality and Fractional Quantum Hall
... stems from exact diagonalization (ED) of small clusters for C = 1 [17–30] and C > 1 [31–35], mutatis-mutandis mappings of the Hilbert space of flat Chern bands to the lowest Landau level (LLL) [15, 36–40] or vice versa [16], and approximate long-wavelength projected density algebra [41–48]. The latt ...
... stems from exact diagonalization (ED) of small clusters for C = 1 [17–30] and C > 1 [31–35], mutatis-mutandis mappings of the Hilbert space of flat Chern bands to the lowest Landau level (LLL) [15, 36–40] or vice versa [16], and approximate long-wavelength projected density algebra [41–48]. The latt ...
