410
E. J. Brändas
5 Evolution and Quantum Theory
A living system is characterized by (a) its dissipative coupling to the environment,
(b) its metabolic processes, (c) the genetic function or higher order molecular function and (d) homeostasis for appropriate spatio-temporal regulation. Without going
into detail how a biological system, such as a cell obtains energy through the various biochemical pathways, we will begin to model the biological process via the
concept of the Universal Device U D(n), but with some added properties commensurate with (a-d) above. Obviously, the device agrees with (a) and (b) yielding an
unambiguous output. However, point (c) imparts a self-referential adaptation that
is a fundamentally trait of all life forms, missing in the present laws of physics.
Moreover, what is not known here is how energy exchanges, related to metabolism,
transduce the information that emerges for instance in the genetic code and its associated spatio-temporal regulation mechanism. Whereas the appliances in engineering eventually wears out after good and loyal service, and while these dimensiondetermining limitations are usually not displayed in the mandatory parameters that
controls the behaviour of the device, an U D(n) adapts its generic approach thermally
and spatio-temporally as will be seen in more detail in the next section.
According to the transcripts of the Gran Canaria debate [25], the relevancy of
primary quantum aspects must be proved to be essential for the understanding of all
life processes and its quantum chemical origin. Since in vivo systems are dissipative,
pioneering QM is not adequate to describe an U D(n). In fact, the resonance picture
of so-called unstable states in the continuum, such as e.g. Gamow waves associated
with quantum tunnelling or the resonance formation of quasi-bound states appearing in total- or differential cross sections, are, strictly speaking, outside the domain
of Hilbert Space quantum mechanics. Conceding that scattering theory approaches
belong to traditional quantum mechanics, yet the cross-section peaks, for details see
Ref. [63] and Fig. 2, associated with the continuous part of the energy spectrum,
reflect the existence of complex poles in the Greens function, located on a second
sheet of the complex energy plane.
33 The location of the resonance structure embedded in the continuum commands non-trivial extensions to non-Hermitian quantum
mechanics [21, 37–39]. The latter is a consequence of the Balslev-Combes theorem
for dilation analytic families of Hamiltonians [37] leading to the popular complex
scaling technique in quantum chemical applications [38, 39]. The idea is very simple. It starts with the concept of scaling, a unitary operation in quantum mechanics
and a fundamental method in proving quantum virial relations.
34 Making the dilation parameter complex yields surprising consequences: Hermitian operators, after
complex scaling, become non-Hermitian and importantly non-normal, i.e. not commuting with their own adjoints; time evolution is no longer a unitary operation,
35
and the poles of the resolvent, see Eq. (4.11) below, may leave the real energy axis.
33 This is usually referred to as analytic continuation onto the second unphysical Riemann sheet.
34 For instance the relation between kinetic and potential energies, see relevant discussions in Ref.
[26].
35 Cf. the concept of star-unitary transformations introduced by the Brussels-Austin School.
E. J. Brändas
5 Evolution and Quantum Theory
A living system is characterized by (a) its dissipative coupling to the environment,
(b) its metabolic processes, (c) the genetic function or higher order molecular function and (d) homeostasis for appropriate spatio-temporal regulation. Without going
into detail how a biological system, such as a cell obtains energy through the various biochemical pathways, we will begin to model the biological process via the
concept of the Universal Device U D(n), but with some added properties commensurate with (a-d) above. Obviously, the device agrees with (a) and (b) yielding an
unambiguous output. However, point (c) imparts a self-referential adaptation that
is a fundamentally trait of all life forms, missing in the present laws of physics.
Moreover, what is not known here is how energy exchanges, related to metabolism,
transduce the information that emerges for instance in the genetic code and its associated spatio-temporal regulation mechanism. Whereas the appliances in engineering eventually wears out after good and loyal service, and while these dimensiondetermining limitations are usually not displayed in the mandatory parameters that
controls the behaviour of the device, an U D(n) adapts its generic approach thermally
and spatio-temporally as will be seen in more detail in the next section.
According to the transcripts of the Gran Canaria debate [25], the relevancy of
primary quantum aspects must be proved to be essential for the understanding of all
life processes and its quantum chemical origin. Since in vivo systems are dissipative,
pioneering QM is not adequate to describe an U D(n). In fact, the resonance picture
of so-called unstable states in the continuum, such as e.g. Gamow waves associated
with quantum tunnelling or the resonance formation of quasi-bound states appearing in total- or differential cross sections, are, strictly speaking, outside the domain
of Hilbert Space quantum mechanics. Conceding that scattering theory approaches
belong to traditional quantum mechanics, yet the cross-section peaks, for details see
Ref. [63] and Fig. 2, associated with the continuous part of the energy spectrum,
reflect the existence of complex poles in the Greens function, located on a second
sheet of the complex energy plane.
33 The location of the resonance structure embedded in the continuum commands non-trivial extensions to non-Hermitian quantum
mechanics [21, 37–39]. The latter is a consequence of the Balslev-Combes theorem
for dilation analytic families of Hamiltonians [37] leading to the popular complex
scaling technique in quantum chemical applications [38, 39]. The idea is very simple. It starts with the concept of scaling, a unitary operation in quantum mechanics
and a fundamental method in proving quantum virial relations.
34 Making the dilation parameter complex yields surprising consequences: Hermitian operators, after
complex scaling, become non-Hermitian and importantly non-normal, i.e. not commuting with their own adjoints; time evolution is no longer a unitary operation,
35
and the poles of the resolvent, see Eq. (4.11) below, may leave the real energy axis.
33 This is usually referred to as analytic continuation onto the second unphysical Riemann sheet.
34 For instance the relation between kinetic and potential energies, see relevant discussions in Ref.
[26].
35 Cf. the concept of star-unitary transformations introduced by the Brussels-Austin School.