In international culinary history, Germany is still largely a blank space, its unparalleled wealth of source material and large body of published research available only to readers of German. This ...books aims to give everybody else an overview of German foodways at a crucial juncture in its history. The Reformation era, broadly speaking from the Imperial Reforms of the 1480s to the beginning of the Thirty Years’ War, laid the foundations for many developments in German culture, language, and history, not least the notion of its existence as a country. Understanding the food traditions and habits of the time is important to anyone studying Germany’s culinary history and identity. Using original source material, food production, processing and consumption are explored with a view to the social significance of food and the practicalities of feeding a growing population. Food habits across the social spectrum are presented, looking at the foodways of rich and poor in city and country. The study shows a foodscape richly differentiated by region, class, income, gender and religion, but united by a shared culinary identity that was just beginning to emerge. An appendix of recipes helps the reader gain an appreciation of the practical aspects of food in the age of Martin Luther.
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and ...allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we impose ...an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives, and the interactions between the radiation field and electrons localized very far from the nuclei are turned off. For a class of Hamiltonians we prove exponential localization of bound states, establish the existence of a ground state, and derive sufficient conditions for its uniqueness. Furthermore, we show that excited bound states of the unperturbed system become unstable and turn into resonances when the electrons are coupled to the radiation field. To this end we develop a novel renormalization transformation which acts directly on the space of Hamiltonians.
In this paper we present a self-contained and detailed exposition of the new renormalization group technique proposed in 1, 2. Its main feature is that the renormalization group transformation acts ...directly on a space of operators rather than on objects such as a propagator, the partition function, or correlation functions. We apply this renormalization transformation to a Hamiltonian describing the physics of an atom interacting with the quantized electromagnetic field, and we prove that excited atomic states turn into resonances when the coupling between electrons and field is nonvanishing.
Two decades ago, Lieb and Loss (Self-energy of electrons in non-perturbative QED. Preprint
arXiv:math-ph/9908020
and mp-arc #99–305, 1999) approximated the ground state energy of a free, ...nonrelativistic electron coupled to the quantized radiation field by the infimum
E
α
,
Λ
of all expectation values
⟨
ϕ
el
⊗
ψ
ph
|
H
α
,
Λ
(
ϕ
el
⊗
ψ
ph
)
⟩
, where
H
α
,
Λ
is the corresponding Hamiltonian with fine structure constant
α
>
0
and ultraviolet cutoff
Λ
<
∞
, and
ϕ
el
and
ψ
ph
are normalized electron and photon wave functions, respectively. Lieb and Loss showed that
c
α
1
/
2
Λ
3
/
2
≤
E
α
,
Λ
≤
c
-
1
α
2
/
7
Λ
12
/
7
for some constant
c
>
0
. In the present paper, we prove the existence of a constant
C
<
∞
, such that
|
E
α
,
Λ
F
1
α
2
/
7
Λ
12
/
7
-
1
|
≤
C
α
4
/
105
Λ
-
4
/
105
holds true, where
F
1
>
0
is an explicit universal number. This result shows that Lieb and Loss’ upper bound is actually sharp and gives the asymptotics of
E
α
,
Λ
uniformly in the limit
α
→
0
and in the ultraviolet limit
Λ
→
∞
.
Thumb Bibles Adam, Gottfried
2022, Letnik:
108
eBook
Thumb bibles are a previously unexplored genre of miniature books. This study examines them from a theological, literary, book-historical and pious perspective.
We consider a finite-dimensional quantum system coupled to the bosonic radiation field and subject to a time-periodic control operator. Assuming the validity of a certain dynamic decoupling ...condition, we approximate the system’s time evolution with respect to the non-interacting dynamics. For sufficiently small coupling constants
g
and control periods
T
, we show that a certain deviation of coupled and uncoupled propagator may be estimated by
O
(
g
t
T
)
. Our approach relies on the concept of Kato stability and general theory on non-autonomous linear evolution equations.
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