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1.
Jun Yin 《Communications in Mathematical Physics》2010,295(1):1-27
The leading term of the ground state energy/particle of a dilute gas of bosons with mass m in the thermodynamic limit is 2p(h/2p)2 a r/m{2\pi \hbar^2 a \varrho/m} when the density of the gas is r{\varrho}, the interaction potential is non-negative and the scattering length a is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive
scattering length, i.e, a > 0 and the lower bound part to some interaction potentials with shallow and/or narrow negative parts. 相似文献
2.
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to
the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy
levels of the physical system. We consider the case when the n×n external source matrix has two distinct real eigenvalues: a with multiplicity r and zero with multiplicity n−r. For a Gaussian potential, it was shown by Péché (Probab. Theory Relat. Fields 134:127–173, 2006) that when r is fixed or grows sufficiently slowly with n (a small-rank source), r eigenvalues are expected to exit the main bulk for |a| large enough. Furthermore, at the critical value of a when the outliers are at the edge of a band, the eigenvalues at the edge are described by the r-Airy kernel. We establish the universality of the r-Airy kernel for a general class of analytic potentials for r=O(ng)r=\mathcal{O}(n^{\gamma}) for 0≤γ<1/12. 相似文献
3.
Horizontal rolls, generated in convective flow above a partially heated bottom in a
rectangular box are studied experimentally for a wide range of the Prandtl number
(7 ≤ P
r ≤ 1020), the Rayleigh number
(300 ≤ R
a ≤ 2.8 × 107) and the aspect ratio
(0.08 ≤ a ≤ 0.7). Experimental studies are supported by direct
numerical simulations, which made possible the examination of the regimes inaccessible in
the experiment, and also to investigate in detail the heat transfer in the convective
flow. A variety of regimes with longitudinal helical rolls, with transverse rolls and with
mixed structures has been observed. The structure of secondary flows is defined by the
level of convective supercriticality in the boundary layer (Rayleigh number) and the
intensity of the throughflow, defined by the Reynolds number, which depends itself on the
heating and size, i.e. on the Rayleigh number. Most of the studied regimes were
characterized by the appearance of longitudinal rolls. The transverse rolls appear in the
flow only under the conditions of the large vertical drop in the temperature and weak
large-scale flow (that is possible only at large values of the Prandtl number). Both
longitudinal and transverse rolls lead to remarkable heat transfer enhancement. The
formation and characteristics of horizontal rolls are described in details. 相似文献
4.
E. Kyriakopoulos 《General Relativity and Gravitation》2012,44(1):157-199
We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and
applying the “Newman–Janis complex coordinate trick” we get a rotating metric g
μν
with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q
E
and magnetic Q
M
. Then we find a solution of the equations of motion having this g
μν
as metric. Our solution is asymptotically flat and has angular momentum J = M
a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics,
the vector fields and the quantity l = x+ie-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q
E
, Sen for Q
E
and Q
M
, Kerr–Newman for Q
E
and Q
M
, Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild
are the same function of a, and two functions ρ
2 = r(r + b) + a
2 cos2
θ and Δ = r(r + b) − 2Mr + a
2 + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown
that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and
that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions
outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and
for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another
a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most
physically interesting and well known solutions, are listed in an “Appendix”. 相似文献
5.
B. Ananthanarayan S. Ramanan 《The European Physical Journal C - Particles and Fields》2009,60(1):73-81
The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like
region, 4m
π
2≤t≤t
in and its value at one space-like point, using as input the (g−2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the
corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors
present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results
for c. We obtain
when c is set to the chiral perturbation-theory values. 相似文献
6.
The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤g
KNΛ≤−3.67 and 1.15 ≤g
KNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K
*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants g
KNΛ and g
KNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction
and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings.
Received: 17 August 1998 / Revised version: 22 December 1998 相似文献
7.
It is suggested that the strength of nuclear colour van der Waals interaction, if present, can be determined by measuring
deviations from Rutherford scattering of charged hadrons from nuclei, at energies well below the Coulomb barrier. Experimental
limit on the strength of such a potential is obtained asλ<50, when the colour van der Waals potential is given byV(r)=λ(hc/r
0)(r
0/r)7, withr
0, the scaling length, taken as 1 fm. This limit is obtained from an analysis of existing experiments and by performing scattering
experiments of 3–4.6 MeV protons from a208Pb target. 相似文献
8.
We present a mathematically rigorous analysis of the ground state of a dilute, interacting Bose gas in a three-dimensional trap that is strongly confining in one direction so that the system becomes effectively two-dimensional. The parameters involved are the particle number, , the two-dimensional extension, , of the gas cloud in the trap, the thickness, of the trap, and the scattering length a of the interaction potential. Our analysis starts from the full many-body Hamiltonian with an interaction potential that is assumed to be repulsive, radially symmetric and of short range, but otherwise arbitrary. In particular, hard cores are allowed. Under the premises that the confining energy, ~ 1/h
2, is much larger than the internal energy per particle, and a/h→ 0, we prove that the system can be treated as a gas of two-dimensional bosons with scattering length a
2D = hexp(−(const.)h/a). In the parameter region where , with the mean density, the system is described by a two-dimensional Gross-Pitaevskii density functional with coupling parameter ~ Na/h. If the coupling parameter is and thus independent of a. In both cases Bose-Einstein condensation in the ground state holds, provided the coupling parameter stays bounded. 相似文献
9.
We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a
2, with a
2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude
whose low-momentum part is renormalization-group invariant up to corrections of O(R
3/a
2
3). Since corrections of O(R/a
2) and O(R
2/a
2
2) can be straightforwardly included in the integral equation’s kernel, a unique solution for 1 + 2 scattering phase shifts
and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation
between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement
with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials. 相似文献
10.
11.
The axio-electric effect in silicon atoms is sought for solar axions appearing owing to bremsstrahlung and the Compton process. Axions are detected using a Si(Li) detector placed in a low-background setup. As a result, a model-independent constraint on the axion-electron coupling constant |g Ae | ≤ 2.2 × 10−10 has been obtained, which leads to the bounds m A ≤ 7.9 eV and m A ≤ 1.4 eV (at 90% C.L.) for the mass of the axion in the DFSZ and KSVZ models, respectively. 相似文献
12.
We use different determinantal Hartree-Fock (HF) wave functions to calculate true variational upper bounds for the ground
state energy of N spin-half fermions in volume V
0, with mass m, electric charge zero, and magnetic moment μ, interacting through magnetic dipole-dipole interaction. We find that at high
densities when the average interparticle distance r
0 becomes small compared to the magnetic length r
m ≡ 2mμ2/ħ2, a ferromagnetic state with spheroidal occupation function n
↑(), involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic
state or for the state with dipolar deformation. This system is unstable towards infinite density collapse, but we show explicitly
that a suitable short-range repulsive (hard core) interaction of strength U
0 and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation
function is possible as long as the ratio of coupling constants Γcm ≡ (U
0
a
3/μ2) is not very small compared to 1.
相似文献
13.
Jai Kumar Singhal 《Pramana》2004,62(5):1029-1040
We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the
process l+l− →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s
= Λ), we obtain bounds on light heavy charged lepton mixing parameter sin2(2θ
L
a
) where θ
L
a
is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin2 (2θ
L
a
) form
E < 0.69 TeV. However, sin2 (2θ
L
a
) ≤ 1.52×10−5 form
E = 5 TeV, sin2 (2θ
L
a
) ≤ 2.41 ×10−7 form
E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin2 (2θ
L
a
) for mE < 1.97 TeV and sin2 (2θ
L
a
) ≤ 0.15 form
E = 5 TeV and sin2 (2θ
L
a
) ≤ 3.88×10-2 form
E = 10 TeV. 相似文献
14.
We calculate the process np → ηd near threshold using a separable potential model of the coupled ηN - πN - ππN subystems, and a relativistic three-body calculation for the ηd scattering amplitude. The ππN channels are represented by an effective σN channel, and we compare the case where the σ and π masses are related by m
σ = 2m
π and no width is considered, to another where the mass and width of the σ -meson are taken from ππ scattering data. The np → ηd cross-section can be well described up to about 60MeV by models where the real part of the ηN scattering length lies between 0.4≤Re(a
ηN)≤0.6 fm which allows us to determine the s -wave ηN scattering amplitude for -60≤E≤60 MeV. 相似文献
15.
Utpal Mukhopadhyay Partha Pratim Ghosh Saibal Ray 《International Journal of Theoretical Physics》2010,49(7):1622-1627
Two phenomenological models of Λ, viz. L ~ ([(a)\dot]/a)2\Lambda \sim (\dot{a}/a)^{2} and L ~ [(a)\ddot]/a\Lambda \sim \ddot{a}/a are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time as suggested earlier by others including Dirac. The models considered here can be matched
with observational results by properly tuning the parameters of the models. Our analysis shows that L ~ [(a)\ddot]/a\Lambda \sim \ddot{a}/a model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The
other model L ~ ([(a)\dot]/a)2\Lambda \sim (\dot{a}/a)^{2} is, in general, attractive in nature. Moreover, it is seen that due to the combined effect of time-variable Λ and G the Universe evolved with acceleration as well as deceleration. This later one indicates a Big Crunch. 相似文献
16.
K. Lal S. K. Chattopadhyay A. K. Meikap S. K. Chatterjee M. Ghosh 《Czechoslovak Journal of Physics》2001,51(9):897-908
A detailed study on the weak localization phenomenon vis-a-vis electron-electron interaction effects in magnetic metallic
glasses has been carried out. We measured the electrical conductivity and magnetoconductivity within the temperature range
1.8≤T≤300K. A maximum on the conductivity versus temperature curve exists atT=T
m. The conductivity was observed to follow aT
1/2 law forT<T
m andT
2 law forT>T
m. Magnetoconductivity data of these alloys indicate the prominence of electron-electron interaction at low temperatures. The
authors have determined the inelastic scattering field and spin-orbit scattering field from the magnetoconductivity data.
The inelastic scattering field obeys aT
p law (p=2) at low temperatures. 相似文献
17.
R. Haussmann 《Zeitschrift für Physik B Condensed Matter》1993,91(3):291-308
A dilute three-dimensional Fermi liquid is considered with an instantaneous attractive short-range interaction. Two sets of self-consistent equations for the temperature dependent fermion Greens functiong and the four-point vertex function are derived by field theoretic means. The interaction is taken into account using the results of low energys-wave scattering theory. The crossover region between BCS superconductivity and Bose-Einstein condensation of tightly bound pairs is located near the threshold where in the two-particle scattering problem a virtual or quasi-stationary state turns into a bound state. We show how from our self-consistent equations the BCS theory and the theory of a superfluid Bose gas can be recovered in the weak and strong coupling limit, respectively. In the strong coupling limit we find that there is a repulsive interaction between the composite bosons due to the Pauli exclusion principle. It is described by a positive scattering lengtha
B
which is twice the scattering length of the fermions,a
B
=2a
F
. Furthermore we find that this interaction reduces the Bose-Einstein transition temperature to leading order by T
c
/T
c, BE
=–(k
F
a
F
)3/3. We show that most of the previous theories of the crossover scenario can be obtained from our theory in mean-field approximation neglecting self consistency. 相似文献
18.
C?t?lin I. Carstea 《Communications in Mathematical Physics》2010,300(2):487-528
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from
\mathbbR2+1 ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d
ρ
2 + g(ρ)2
dθ2, g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u
tt
+ u
rr
+ r
−1
u
r
= r
−2
g(u)g′(u), λ(t) = t
−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0. 相似文献
19.
A. D. Smirnov 《Optics and Spectroscopy》2010,109(5):680-686
Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients,
oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A
1Σ
u
+-X
1Σ
g
+ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B
1Π
u
-X
1Σ
g
+ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer,
are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated
spectroscopic constants and radiative lifetimes are compared to the experimental values. 相似文献
20.
Kinetic processes taking place in the atomic-molecular system O-O2-O3 in the middle atmosphere with the participation of oxygen molecules in the excited electronic states O2(a
1Δg) and O2(b
1Σ
g
+
) are analyzed in detail. The possibility of increased ozone production under the influence of solar radiation during the
laser excitation of O2 molecules in the a
1Δg state is demonstrated on the basis of numerical modeling. Upper and lower bounds are determined for the densities of O2(a
1Δg) molecules at which the ozone concentration increases in the irradiated zone.
Zh. Tekh. Fiz. 68, 15–23 (August 1998) 相似文献